• Re: Correcting logic to make it a system of correct reasoning

    From Richard Damon@21:1/5 to olcott on Fri May 13 13:47:51 2022
    XPost: comp.theory, sci.logic, sci.lang.semantics

    On 5/13/22 1:20 PM, olcott wrote:
    *Validity and Soundness*
    A deductive argument is said to be valid if and only if it takes a form
    that makes it impossible for the premises to be true and the conclusion nevertheless to be false. Otherwise, a deductive argument is said to be invalid. https://iep.utm.edu/val-snd/

    If the Moon is made of green cheese then all dogs are cats is valid and
    even though premises and conclusion are semantically unrelated.

    *Here is my correction to that issue*
    A deductive argument is said to be valid if and only if it takes a form
    such that its conclusion is a necessary consequence of all of its premises.


    And, have you done the basic investigation to find out how much of
    conventional logic you invalidate with that change?

    Note, that it may be hard to define "necessary consequence" in a formal
    matter.

    It should be noted that your example, while considered an vaild
    inference by normal logic, can never be used to actually prove its
    conclusion, so doesn't actually cause problems in normal logic (can you
    show a case where it does?)

    Note, that at least by some meanings of your words, it could be
    construed that you only accept as a correct deductive argument, and
    arguement whose premises can at least some times be true, but there are
    some statements we don't know if they CAN be sometimes true, so your
    logic system would seem to not allow doing logic with that sort of
    statement.

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  • From olcott@21:1/5 to Richard Damon on Fri May 13 13:10:36 2022
    XPost: comp.theory, sci.logic, sci.lang.semantics

    On 5/13/2022 12:47 PM, Richard Damon wrote:
    On 5/13/22 1:20 PM, olcott wrote:
    *Validity and Soundness*
    A deductive argument is said to be valid if and only if it takes a
    form that makes it impossible for the premises to be true and the
    conclusion nevertheless to be false. Otherwise, a deductive argument
    is said to be invalid. https://iep.utm.edu/val-snd/

    If the Moon is made of green cheese then all dogs are cats is valid
    and even though premises and conclusion are semantically unrelated.

    *Here is my correction to that issue*
    A deductive argument is said to be valid if and only if it takes a
    form such that its conclusion is a necessary consequence of all of its
    premises.


    And, have you done the basic investigation to find out how much of conventional logic you invalidate with that change?


    It categorically changes everything that is broken.

    Note, that it may be hard to define "necessary consequence" in a formal matter.


    {A,B} ⊢ C only when truth preserving operations are applied to {A,B} to derive C.

    It should be noted that your example, while considered an vaild
    inference by normal logic, can never be used to actually prove its conclusion, so doesn't actually cause problems in normal logic (can you
    show a case where it does?)


    With my correction true and unprovable is impossible, unprovable simply
    means untrue.

    Note, that at least by some meanings of your words, it could be
    construed that you only accept as a correct deductive argument, and
    arguement whose premises can at least some times be true, but there are
    some statements we don't know if they CAN be sometimes true, so your
    logic system would seem to not allow doing logic with that sort of
    statement.


    An analytic statement is only known to be true when it is derived by
    applying only truth preserving operations to all of its premises and all
    of its premises are known to be true, otherwise its truth value is unknown.



    --
    Copyright 2022 Pete Olcott

    "Talent hits a target no one else can hit;
    Genius hits a target no one else can see."
    Arthur Schopenhauer

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  • From olcott@21:1/5 to All on Fri May 13 12:20:48 2022
    XPost: comp.theory, sci.logic, sci.lang.semantics

    *Validity and Soundness*
    A deductive argument is said to be valid if and only if it takes a form
    that makes it impossible for the premises to be true and the conclusion nevertheless to be false. Otherwise, a deductive argument is said to be invalid. https://iep.utm.edu/val-snd/

    If the Moon is made of green cheese then all dogs are cats is valid and
    even though premises and conclusion are semantically unrelated.

    *Here is my correction to that issue*
    A deductive argument is said to be valid if and only if it takes a form
    such that its conclusion is a necessary consequence of all of its premises.




    --
    Copyright 2022 Pete Olcott

    "Talent hits a target no one else can hit;
    Genius hits a target no one else can see."
    Arthur Schopenhauer

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From =?UTF-8?B?QW5kcsOpIEcuIElzYWFr?=@21:1/5 to olcott on Fri May 13 12:28:22 2022
    XPost: comp.theory, sci.logic, sci.lang.semantics

    On 2022-05-13 11:20, olcott wrote:
    *Validity and Soundness*
    A deductive argument is said to be valid if and only if it takes a form
    that makes it impossible for the premises to be true and the conclusion nevertheless to be false. Otherwise, a deductive argument is said to be invalid. https://iep.utm.edu/val-snd/

    If the Moon is made of green cheese then all dogs are cats is valid and
    even though premises and conclusion are semantically unrelated.

    That isn't valid. Perhaps you should learn what 'valid' actually means
    before you attempt to "correct" the definition.

    [Also, the above isn't even an argument. It is simply a conditional
    statement. It has no conclusion].

    *Here is my correction to that issue*
    A deductive argument is said to be valid if and only if it takes a form
    such that its conclusion is a necessary consequence of all of its premises.

    And that differs from the standard definition how exactly? Unless you
    have some special personal meaning for 'necessary consequence' it would
    appear to be simply a paraphrase of the definition you cite above.

    André


    --
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    service.

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  • From olcott@21:1/5 to All on Fri May 13 13:50:35 2022
    XPost: comp.theory, sci.logic, sci.lang.semantics

    On 5/13/2022 1:28 PM, André G. Isaak wrote:
    On 2022-05-13 11:20, olcott wrote:
    *Validity and Soundness*
    A deductive argument is said to be valid if and only if it takes a
    form that makes it impossible for the premises to be true and the
    conclusion nevertheless to be false. Otherwise, a deductive argument
    is said to be invalid. https://iep.utm.edu/val-snd/

    If the Moon is made of green cheese then all dogs are cats is valid
    and even though premises and conclusion are semantically unrelated.

    That isn't valid. Perhaps you should learn what 'valid' actually means
    before you attempt to "correct" the definition.

    [Also, the above isn't even an argument. It is simply a conditional statement. It has no conclusion].


    (a) The Moon is made of green cheese.
    (b) Water is a kind of concrete.
    (c) Therefore all dogs are cats.

    Because the premises are false and the conclusion is false it is not a
    case of the conclusion is true and the premises are false, thus meets
    the above validity criteria.

    *Here is my correction to that issue*
    A deductive argument is said to be valid if and only if it takes a
    form such that its conclusion is a necessary consequence of all of its
    premises.

    And that differs from the standard definition how exactly? Unless you
    have some special personal meaning for 'necessary consequence' it would

    Semantic relevance is a key aspect of 'necessary consequence'.

    appear to be simply a paraphrase of the definition you cite above.

    André




    --
    Copyright 2022 Pete Olcott

    "Talent hits a target no one else can hit;
    Genius hits a target no one else can see."
    Arthur Schopenhauer

    --- SoupGate-Win32 v1.05
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  • From =?UTF-8?B?QW5kcsOpIEcuIElzYWFr?=@21:1/5 to olcott on Fri May 13 13:00:03 2022
    XPost: comp.theory, sci.logic, sci.lang.semantics

    On 2022-05-13 12:50, olcott wrote:
    On 5/13/2022 1:28 PM, André G. Isaak wrote:
    On 2022-05-13 11:20, olcott wrote:
    *Validity and Soundness*
    A deductive argument is said to be valid if and only if it takes a
    form that makes it impossible for the premises to be true and the
    conclusion nevertheless to be false. Otherwise, a deductive argument
    is said to be invalid. https://iep.utm.edu/val-snd/

    If the Moon is made of green cheese then all dogs are cats is valid
    and even though premises and conclusion are semantically unrelated.

    That isn't valid. Perhaps you should learn what 'valid' actually means
    before you attempt to "correct" the definition.

    [Also, the above isn't even an argument. It is simply a conditional
    statement. It has no conclusion].


    (a) The Moon is made of green cheese.
    (b) Water is a kind of concrete.
    (c) Therefore all dogs are cats.

    Because the premises are false and the conclusion is false it is not a
    case of the conclusion is true and the premises are false, thus meets
    the above validity criteria.

    No. It isn't valid. You don't seem to grasp the concept of validity.

    Logic has no concept of whether, for example, the moon is made of green
    cheese. An argument is valid if there is no truth *assignment* under
    which the premises are true and the conclusion is false. The actual
    truth values of these expressions don't play a role in the definition of validity.

    *Here is my correction to that issue*
    A deductive argument is said to be valid if and only if it takes a
    form such that its conclusion is a necessary consequence of all of
    its premises.

    And that differs from the standard definition how exactly? Unless you
    have some special personal meaning for 'necessary consequence' it would

    Semantic relevance is a key aspect of 'necessary consequence'.

    Defined how exactly?

    André

    --
    To email remove 'invalid' & replace 'gm' with well known Google mail
    service.

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From olcott@21:1/5 to All on Fri May 13 14:11:50 2022
    XPost: comp.theory, sci.logic, sci.lang.semantics

    On 5/13/2022 2:00 PM, André G. Isaak wrote:
    On 2022-05-13 12:50, olcott wrote:
    On 5/13/2022 1:28 PM, André G. Isaak wrote:
    On 2022-05-13 11:20, olcott wrote:
    *Validity and Soundness*
    A deductive argument is said to be valid if and only if it takes a
    form that makes it impossible for the premises to be true and the
    conclusion nevertheless to be false. Otherwise, a deductive argument
    is said to be invalid. https://iep.utm.edu/val-snd/

    If the Moon is made of green cheese then all dogs are cats is valid
    and even though premises and conclusion are semantically unrelated.

    That isn't valid. Perhaps you should learn what 'valid' actually
    means before you attempt to "correct" the definition.

    [Also, the above isn't even an argument. It is simply a conditional
    statement. It has no conclusion].


    (a) The Moon is made of green cheese.
    (b) Water is a kind of concrete.
    (c) Therefore all dogs are cats.

    Because the premises are false and the conclusion is false it is not a
    case of the conclusion is true and the premises are false, thus meets
    the above validity criteria.

    No. It isn't valid. You don't seem to grasp the concept of validity.

    Logic has no concept of whether, for example, the moon is made of green cheese. An argument is valid if there is no truth *assignment* under
    which the premises are true and the conclusion is false. The actual
    truth values of these expressions don't play a role in the definition of validity.


    I reach my key insights by progressively refining very high level
    abstractions into their corresponding concrete examples.

    Clearly I have not yet translated this abstraction:

    A deductive argument is said to be valid if and only if it takes a form
    such that its conclusion is a necessary consequence of all of its premises.

    Into a concrete example of the issue that it corrects, quite yet.

    *Here is my correction to that issue*
    A deductive argument is said to be valid if and only if it takes a
    form such that its conclusion is a necessary consequence of all of
    its premises.

    And that differs from the standard definition how exactly? Unless you
    have some special personal meaning for 'necessary consequence' it would

    Semantic relevance is a key aspect of 'necessary consequence'.

    Defined how exactly?

    André


    Here is the original way that semantic relevance was defined:
    Semantically unrelated premises and conclusion is not possible with
    syllogisms. https://en.wikipedia.org/wiki/Syllogism#Basic_structure

    Because syllogisms are comprised of https://en.wikipedia.org/wiki/Categorical_proposition




    --
    Copyright 2022 Pete Olcott

    "Talent hits a target no one else can hit;
    Genius hits a target no one else can see."
    Arthur Schopenhauer

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Richard Damon@21:1/5 to olcott on Fri May 13 15:13:33 2022
    XPost: comp.theory, sci.logic, sci.lang.semantics

    On 5/13/22 2:10 PM, olcott wrote:
    On 5/13/2022 12:47 PM, Richard Damon wrote:
    On 5/13/22 1:20 PM, olcott wrote:
    *Validity and Soundness*
    A deductive argument is said to be valid if and only if it takes a
    form that makes it impossible for the premises to be true and the
    conclusion nevertheless to be false. Otherwise, a deductive argument
    is said to be invalid. https://iep.utm.edu/val-snd/

    If the Moon is made of green cheese then all dogs are cats is valid
    and even though premises and conclusion are semantically unrelated.

    *Here is my correction to that issue*
    A deductive argument is said to be valid if and only if it takes a
    form such that its conclusion is a necessary consequence of all of
    its premises.


    And, have you done the basic investigation to find out how much of
    conventional logic you invalidate with that change?


    It categorically changes everything that is broken.

    So, you are saying we need to throw out EVERYTHING we know and start over?

    I think, especially with the comment below, people will decide that your
    "new" logic systm isn't worth the cost to switch to.


    Note, that it may be hard to define "necessary consequence" in a
    formal matter.


    {A,B} ⊢ C only when truth preserving operations are applied to {A,B} to derive C.

    And what do you define truth perserving as?

    Normally the phrase means that True Premises always generate True
    Results (which means the statement "If the moon is made of green cheese
    then ll dogs are cats" IS Truth Preserving, since any time the premise
    is true (never) the conclusion is true.


    It should be noted that your example, while considered an vaild
    inference by normal logic, can never be used to actually prove its
    conclusion, so doesn't actually cause problems in normal logic (can
    you show a case where it does?)


    With my correction true and unprovable is impossible, unprovable simply
    means untrue.


    Ok, then you have just stated that your new logic system can't handle mathematics, and thus "Computer SCience" no longer exists as a logical
    system.

    This makes you system not much more than a toy for most people.

    Note, that at least by some meanings of your words, it could be
    construed that you only accept as a correct deductive argument, and
    arguement whose premises can at least some times be true, but there
    are some statements we don't know if they CAN be sometimes true, so
    your logic system would seem to not allow doing logic with that sort
    of statement.


    An analytic statement is only known to be true when it is derived by
    applying only truth preserving operations to all of its premises and all
    of its premises are known to be true, otherwise its truth value is unknown.


    KNOWN to be True, not IS TRUE.

    Your statement even admits that truth value might be unknow, which might
    allow it to even be UNKNOWABLE (maybe just in that system) if it can't
    be proven or refuted.

    There is NOTHING about an analytic statement that says it can only be
    true if it is provable. Note, "its truth value is unknown" doesn't mean
    it doesn't have a truth value, just that we don't know what that value is.

    You are confusing Knowledge with Truth.

    Your whole system is built on a Category Error.

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  • From olcott@21:1/5 to Richard Damon on Fri May 13 14:43:58 2022
    XPost: comp.theory, sci.logic, sci.lang.semantics

    On 5/13/2022 2:13 PM, Richard Damon wrote:
    On 5/13/22 2:10 PM, olcott wrote:
    On 5/13/2022 12:47 PM, Richard Damon wrote:
    On 5/13/22 1:20 PM, olcott wrote:
    *Validity and Soundness*
    A deductive argument is said to be valid if and only if it takes a
    form that makes it impossible for the premises to be true and the
    conclusion nevertheless to be false. Otherwise, a deductive argument
    is said to be invalid. https://iep.utm.edu/val-snd/

    If the Moon is made of green cheese then all dogs are cats is valid
    and even though premises and conclusion are semantically unrelated.

    *Here is my correction to that issue*
    A deductive argument is said to be valid if and only if it takes a
    form such that its conclusion is a necessary consequence of all of
    its premises.


    And, have you done the basic investigation to find out how much of
    conventional logic you invalidate with that change?


    It categorically changes everything that is broken.

    So, you are saying we need to throw out EVERYTHING we know and start over?


    Change everything that diverges from my spec:
    A deductive argument is said to be valid if and only if it takes a form
    such that its conclusion is a necessary consequence of all of its premises.

    I think, especially with the comment below, people will decide that your "new" logic systm isn't worth the cost to switch to.


    Note, that it may be hard to define "necessary consequence" in a
    formal matter.


    {A,B} ⊢ C only when truth preserving operations are applied to {A,B}
    to derive C.

    And what do you define truth perserving as?


    Semantic relevance is maintained.

    Normally the phrase means that True Premises always generate True
    Results (which means the statement "If the moon is made of green cheese
    then ll dogs are cats" IS Truth Preserving, since any time the premise
    is true (never) the conclusion is true.


    It should be noted that your example, while considered an vaild
    inference by normal logic, can never be used to actually prove its
    conclusion, so doesn't actually cause problems in normal logic (can
    you show a case where it does?)


    With my correction true and unprovable is impossible, unprovable
    simply means untrue.


    Ok, then you have just stated that your new logic system can't handle mathematics, and thus "Computer SCience" no longer exists as a logical system.


    It corrects the divergence of classical and symbolic logic from correct reasoning.

    This makes you system not much more than a toy for most people.

    Note, that at least by some meanings of your words, it could be
    construed that you only accept as a correct deductive argument, and
    arguement whose premises can at least some times be true, but there
    are some statements we don't know if they CAN be sometimes true, so
    your logic system would seem to not allow doing logic with that sort
    of statement.


    An analytic statement is only known to be true when it is derived by
    applying only truth preserving operations to all of its premises and
    all of its premises are known to be true, otherwise its truth value is
    unknown.


    KNOWN to be True, not IS TRUE.

    It remains unknown until it is known to be true or false.
    My system only eliminates impossibly true or false.


    Your statement even admits that truth value might be unknow, which might allow it to even be UNKNOWABLE (maybe just in that system) if it can't
    be proven or refuted.


    unprovable in the system means untrue in the system.

    There is NOTHING about an analytic statement that says it can only be
    true if it is provable. Note, "its truth value is unknown" doesn't mean
    it doesn't have a truth value, just that we don't know what that value is.


    Within any formal system unprovable in the system means untrue in the
    system.

    The entire body of analytic truth is constructed only on the basis of
    semantic connections between expressions of language, or expressions
    that are stipulated to have the semantic property of Boolean true.
    Lacking both of these and the expression is untrue.

    Since axioms are provable on the basis that they are axioms then both of
    these factors that make an expression true also make it provable.



    You are confusing Knowledge with Truth.

    Your whole system is built on a Category Error.



    --
    Copyright 2022 Pete Olcott

    "Talent hits a target no one else can hit;
    Genius hits a target no one else can see."
    Arthur Schopenhauer

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From =?UTF-8?B?QW5kcsOpIEcuIElzYWFr?=@21:1/5 to olcott on Fri May 13 13:20:13 2022
    XPost: comp.theory, sci.logic, sci.lang.semantics

    On 2022-05-13 13:11, olcott wrote:
    On 5/13/2022 2:00 PM, André G. Isaak wrote:
    On 2022-05-13 12:50, olcott wrote:
    On 5/13/2022 1:28 PM, André G. Isaak wrote:
    On 2022-05-13 11:20, olcott wrote:
    *Validity and Soundness*
    A deductive argument is said to be valid if and only if it takes a
    form that makes it impossible for the premises to be true and the
    conclusion nevertheless to be false. Otherwise, a deductive
    argument is said to be invalid. https://iep.utm.edu/val-snd/

    If the Moon is made of green cheese then all dogs are cats is valid
    and even though premises and conclusion are semantically unrelated.

    That isn't valid. Perhaps you should learn what 'valid' actually
    means before you attempt to "correct" the definition.

    [Also, the above isn't even an argument. It is simply a conditional
    statement. It has no conclusion].


    (a) The Moon is made of green cheese.
    (b) Water is a kind of concrete.
    (c) Therefore all dogs are cats.

    Because the premises are false and the conclusion is false it is not
    a case of the conclusion is true and the premises are false, thus
    meets the above validity criteria.

    No. It isn't valid. You don't seem to grasp the concept of validity.

    Logic has no concept of whether, for example, the moon is made of
    green cheese. An argument is valid if there is no truth *assignment*
    under which the premises are true and the conclusion is false. The
    actual truth values of these expressions don't play a role in the
    definition of validity.


    I reach my key insights by progressively refining very high level abstractions into their corresponding concrete examples.

    Abstractions are designed to cover a large number of different cases. A concrete example cannot capture an abstraction.

    Clearly I have not yet translated this abstraction:

    A deductive argument is said to be valid if and only if it takes a form
    such that its conclusion is a necessary consequence of all of its premises.

    Into a concrete example of the issue that it corrects, quite yet.

    Are you acknowledging that you haven't the foggiest idea what 'valid'
    means? If you're trying to say more than this, I fail to see what it
    might be.

    *Here is my correction to that issue*
    A deductive argument is said to be valid if and only if it takes a
    form such that its conclusion is a necessary consequence of all of
    its premises.

    And that differs from the standard definition how exactly? Unless
    you have some special personal meaning for 'necessary consequence'
    it would

    Semantic relevance is a key aspect of 'necessary consequence'.

    Defined how exactly?

    André


    Here is the original way that semantic relevance was defined:
    Semantically unrelated premises and conclusion is not possible with syllogisms. https://en.wikipedia.org/wiki/Syllogism#Basic_structure

    Because syllogisms are comprised of https://en.wikipedia.org/wiki/Categorical_proposition

    How exactly do two wikipedia articles provide a definition of 'semantic relevance' when neither article contains the word 'semantic' nor the
    word 'relevance'?

    André

    --
    To email remove 'invalid' & replace 'gm' with well known Google mail
    service.

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From olcott@21:1/5 to All on Fri May 13 14:51:29 2022
    XPost: comp.theory, sci.logic, sci.lang.semantics

    On 5/13/2022 2:20 PM, André G. Isaak wrote:
    On 2022-05-13 13:11, olcott wrote:
    On 5/13/2022 2:00 PM, André G. Isaak wrote:
    On 2022-05-13 12:50, olcott wrote:
    On 5/13/2022 1:28 PM, André G. Isaak wrote:
    On 2022-05-13 11:20, olcott wrote:
    *Validity and Soundness*
    A deductive argument is said to be valid if and only if it takes a >>>>>> form that makes it impossible for the premises to be true and the
    conclusion nevertheless to be false. Otherwise, a deductive
    argument is said to be invalid. https://iep.utm.edu/val-snd/

    If the Moon is made of green cheese then all dogs are cats is
    valid and even though premises and conclusion are semantically
    unrelated.

    That isn't valid. Perhaps you should learn what 'valid' actually
    means before you attempt to "correct" the definition.

    [Also, the above isn't even an argument. It is simply a conditional
    statement. It has no conclusion].


    (a) The Moon is made of green cheese.
    (b) Water is a kind of concrete.
    (c) Therefore all dogs are cats.

    Because the premises are false and the conclusion is false it is not
    a case of the conclusion is true and the premises are false, thus
    meets the above validity criteria.

    No. It isn't valid. You don't seem to grasp the concept of validity.

    Logic has no concept of whether, for example, the moon is made of
    green cheese. An argument is valid if there is no truth *assignment*
    under which the premises are true and the conclusion is false. The
    actual truth values of these expressions don't play a role in the
    definition of validity.


    I reach my key insights by progressively refining very high level
    abstractions into their corresponding concrete examples.

    Abstractions are designed to cover a large number of different cases. A concrete example cannot capture an abstraction.

    Clearly I have not yet translated this abstraction:

    A deductive argument is said to be valid if and only if it takes a
    form such that its conclusion is a necessary consequence of all of its
    premises.

    Into a concrete example of the issue that it corrects, quite yet.

    Are you acknowledging that you haven't the foggiest idea what 'valid'
    means? If you're trying to say more than this, I fail to see what it
    might be.


    I am saying that I am redefining the concept of logical validity to
    eliminate its divergence from correct reasoning.

    A deductive argument is said to be valid if and only if it takes a form
    such that its conclusion is a necessary consequence of all of its premises.

    This requires semantic relevance between the all the premises and the conclusion to be maintained.

    *Here is my correction to that issue*
    A deductive argument is said to be valid if and only if it takes a >>>>>> form such that its conclusion is a necessary consequence of all of >>>>>> its premises.

    And that differs from the standard definition how exactly? Unless
    you have some special personal meaning for 'necessary consequence'
    it would

    Semantic relevance is a key aspect of 'necessary consequence'.

    Defined how exactly?

    André


    Here is the original way that semantic relevance was defined:
    Semantically unrelated premises and conclusion is not possible with
    syllogisms. https://en.wikipedia.org/wiki/Syllogism#Basic_structure

    Because syllogisms are comprised of
    https://en.wikipedia.org/wiki/Categorical_proposition

    How exactly do two wikipedia articles provide a definition of 'semantic relevance' when neither article contains the word 'semantic' nor the
    word 'relevance'?

    André


    https://en.wikipedia.org/wiki/Relevance_logic

    Also it can be easily seen that Categorical_propositions cannot possibly diverge from semantic relevance.


    --
    Copyright 2022 Pete Olcott

    "Talent hits a target no one else can hit;
    Genius hits a target no one else can see."
    Arthur Schopenhauer

    --- SoupGate-Win32 v1.05
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  • From =?UTF-8?B?QW5kcsOpIEcuIElzYWFr?=@21:1/5 to olcott on Fri May 13 14:02:23 2022
    XPost: comp.theory, sci.logic, sci.lang.semantics

    On 2022-05-13 13:51, olcott wrote:
    On 5/13/2022 2:20 PM, André G. Isaak wrote:
    On 2022-05-13 13:11, olcott wrote:
    On 5/13/2022 2:00 PM, André G. Isaak wrote:
    On 2022-05-13 12:50, olcott wrote:
    On 5/13/2022 1:28 PM, André G. Isaak wrote:
    On 2022-05-13 11:20, olcott wrote:
    *Validity and Soundness*
    A deductive argument is said to be valid if and only if it takes >>>>>>> a form that makes it impossible for the premises to be true and
    the conclusion nevertheless to be false. Otherwise, a deductive
    argument is said to be invalid. https://iep.utm.edu/val-snd/

    If the Moon is made of green cheese then all dogs are cats is
    valid and even though premises and conclusion are semantically
    unrelated.

    That isn't valid. Perhaps you should learn what 'valid' actually
    means before you attempt to "correct" the definition.

    [Also, the above isn't even an argument. It is simply a
    conditional statement. It has no conclusion].


    (a) The Moon is made of green cheese.
    (b) Water is a kind of concrete.
    (c) Therefore all dogs are cats.

    Because the premises are false and the conclusion is false it is
    not a case of the conclusion is true and the premises are false,
    thus meets the above validity criteria.

    No. It isn't valid. You don't seem to grasp the concept of validity.

    Logic has no concept of whether, for example, the moon is made of
    green cheese. An argument is valid if there is no truth *assignment*
    under which the premises are true and the conclusion is false. The
    actual truth values of these expressions don't play a role in the
    definition of validity.


    I reach my key insights by progressively refining very high level
    abstractions into their corresponding concrete examples.

    Abstractions are designed to cover a large number of different cases.
    A concrete example cannot capture an abstraction.

    Clearly I have not yet translated this abstraction:

    A deductive argument is said to be valid if and only if it takes a
    form such that its conclusion is a necessary consequence of all of
    its premises.

    Into a concrete example of the issue that it corrects, quite yet.

    Are you acknowledging that you haven't the foggiest idea what 'valid'
    means? If you're trying to say more than this, I fail to see what it
    might be.


    I am saying that I am redefining the concept of logical validity to
    eliminate its divergence from correct reasoning.

    Except you haven't show any instances where it diverges from 'correct reasoning'. You gave an example argument which was *not* valid, claimed
    that it was valid and that this "fact" was somehow a problem. The only
    problem I can see is your failure to grasp what it means for something
    to be valid.

    If you can't even figure out whether an argument is valid or not, you're
    not in any position to claim there is something wrong with the accepted
    concept of validity.

    André

    --
    To email remove 'invalid' & replace 'gm' with well known Google mail
    service.

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  • From Richard Damon@21:1/5 to olcott on Fri May 13 16:03:55 2022
    XPost: comp.theory, sci.logic, sci.lang.semantics

    On 5/13/22 3:11 PM, olcott wrote:
    On 5/13/2022 2:00 PM, André G. Isaak wrote:
    On 2022-05-13 12:50, olcott wrote:
    On 5/13/2022 1:28 PM, André G. Isaak wrote:
    On 2022-05-13 11:20, olcott wrote:
    *Validity and Soundness*
    A deductive argument is said to be valid if and only if it takes a
    form that makes it impossible for the premises to be true and the
    conclusion nevertheless to be false. Otherwise, a deductive
    argument is said to be invalid. https://iep.utm.edu/val-snd/

    If the Moon is made of green cheese then all dogs are cats is valid
    and even though premises and conclusion are semantically unrelated.

    That isn't valid. Perhaps you should learn what 'valid' actually
    means before you attempt to "correct" the definition.

    [Also, the above isn't even an argument. It is simply a conditional
    statement. It has no conclusion].


    (a) The Moon is made of green cheese.
    (b) Water is a kind of concrete.
    (c) Therefore all dogs are cats.

    Because the premises are false and the conclusion is false it is not
    a case of the conclusion is true and the premises are false, thus
    meets the above validity criteria.

    No. It isn't valid. You don't seem to grasp the concept of validity.

    Logic has no concept of whether, for example, the moon is made of
    green cheese. An argument is valid if there is no truth *assignment*
    under which the premises are true and the conclusion is false. The
    actual truth values of these expressions don't play a role in the
    definition of validity.


    I reach my key insights by progressively refining very high level abstractions into their corresponding concrete examples.

    Clearly I have not yet translated this abstraction:

    A deductive argument is said to be valid if and only if it takes a form
    such that its conclusion is a necessary consequence of all of its premises.

    Into a concrete example of the issue that it corrects, quite yet.

    *Here is my correction to that issue*
    A deductive argument is said to be valid if and only if it takes a
    form such that its conclusion is a necessary consequence of all of
    its premises.

    And that differs from the standard definition how exactly? Unless
    you have some special personal meaning for 'necessary consequence'
    it would

    Semantic relevance is a key aspect of 'necessary consequence'.

    Defined how exactly?

    André


    Here is the original way that semantic relevance was defined:
    Semantically unrelated premises and conclusion is not possible with syllogisms. https://en.wikipedia.org/wiki/Syllogism#Basic_structure

    Because syllogisms are comprised of https://en.wikipedia.org/wiki/Categorical_proposition





    My first thought is that if you are going to be limiting your reasoning capability to simple things. You seem to be stuck in using simple logic methods, which will limit what you can actually prove.

    What you don't seem to understand is that much of what we have logically proven, is based on higher order logical systems, which these simple
    forms just can't handle.

    In particular, Computation theory, like much of mathematics, needs
    second order (or higher) logic forms, which the simple logic just can't
    handle.

    --- SoupGate-Win32 v1.05
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  • From olcott@21:1/5 to All on Fri May 13 15:08:24 2022
    XPost: comp.theory, sci.logic, sci.lang.semantics

    On 5/13/2022 3:02 PM, André G. Isaak wrote:
    On 2022-05-13 13:51, olcott wrote:
    On 5/13/2022 2:20 PM, André G. Isaak wrote:
    On 2022-05-13 13:11, olcott wrote:
    On 5/13/2022 2:00 PM, André G. Isaak wrote:
    On 2022-05-13 12:50, olcott wrote:
    On 5/13/2022 1:28 PM, André G. Isaak wrote:
    On 2022-05-13 11:20, olcott wrote:
    *Validity and Soundness*
    A deductive argument is said to be valid if and only if it takes >>>>>>>> a form that makes it impossible for the premises to be true and >>>>>>>> the conclusion nevertheless to be false. Otherwise, a deductive >>>>>>>> argument is said to be invalid. https://iep.utm.edu/val-snd/

    If the Moon is made of green cheese then all dogs are cats is
    valid and even though premises and conclusion are semantically >>>>>>>> unrelated.

    That isn't valid. Perhaps you should learn what 'valid' actually >>>>>>> means before you attempt to "correct" the definition.

    [Also, the above isn't even an argument. It is simply a
    conditional statement. It has no conclusion].


    (a) The Moon is made of green cheese.
    (b) Water is a kind of concrete.
    (c) Therefore all dogs are cats.

    Because the premises are false and the conclusion is false it is
    not a case of the conclusion is true and the premises are false,
    thus meets the above validity criteria.

    No. It isn't valid. You don't seem to grasp the concept of validity. >>>>>
    Logic has no concept of whether, for example, the moon is made of
    green cheese. An argument is valid if there is no truth
    *assignment* under which the premises are true and the conclusion
    is false. The actual truth values of these expressions don't play a
    role in the definition of validity.


    I reach my key insights by progressively refining very high level
    abstractions into their corresponding concrete examples.

    Abstractions are designed to cover a large number of different cases.
    A concrete example cannot capture an abstraction.

    Clearly I have not yet translated this abstraction:

    A deductive argument is said to be valid if and only if it takes a
    form such that its conclusion is a necessary consequence of all of
    its premises.

    Into a concrete example of the issue that it corrects, quite yet.

    Are you acknowledging that you haven't the foggiest idea what 'valid'
    means? If you're trying to say more than this, I fail to see what it
    might be.


    I am saying that I am redefining the concept of logical validity to
    eliminate its divergence from correct reasoning.

    Except you haven't show any instances where it diverges from 'correct reasoning'.

    True and unprovable become impossible because Provable() is an aspect of True().

    You gave an example argument which was *not* valid, claimed
    that it was valid and that this "fact" was somehow a problem. The only problem I can see is your failure to grasp what it means for something
    to be valid.

    If you can't even figure out whether an argument is valid or not, you're
    not in any position to claim there is something wrong with the accepted concept of validity.

    André



    --
    Copyright 2022 Pete Olcott

    "Talent hits a target no one else can hit;
    Genius hits a target no one else can see."
    Arthur Schopenhauer

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  • From olcott@21:1/5 to Richard Damon on Fri May 13 15:14:40 2022
    XPost: comp.theory, sci.logic, sci.lang.semantics

    On 5/13/2022 3:03 PM, Richard Damon wrote:
    On 5/13/22 3:11 PM, olcott wrote:
    On 5/13/2022 2:00 PM, André G. Isaak wrote:
    On 2022-05-13 12:50, olcott wrote:
    On 5/13/2022 1:28 PM, André G. Isaak wrote:
    On 2022-05-13 11:20, olcott wrote:
    *Validity and Soundness*
    A deductive argument is said to be valid if and only if it takes a >>>>>> form that makes it impossible for the premises to be true and the
    conclusion nevertheless to be false. Otherwise, a deductive
    argument is said to be invalid. https://iep.utm.edu/val-snd/

    If the Moon is made of green cheese then all dogs are cats is
    valid and even though premises and conclusion are semantically
    unrelated.

    That isn't valid. Perhaps you should learn what 'valid' actually
    means before you attempt to "correct" the definition.

    [Also, the above isn't even an argument. It is simply a conditional
    statement. It has no conclusion].


    (a) The Moon is made of green cheese.
    (b) Water is a kind of concrete.
    (c) Therefore all dogs are cats.

    Because the premises are false and the conclusion is false it is not
    a case of the conclusion is true and the premises are false, thus
    meets the above validity criteria.

    No. It isn't valid. You don't seem to grasp the concept of validity.

    Logic has no concept of whether, for example, the moon is made of
    green cheese. An argument is valid if there is no truth *assignment*
    under which the premises are true and the conclusion is false. The
    actual truth values of these expressions don't play a role in the
    definition of validity.


    I reach my key insights by progressively refining very high level
    abstractions into their corresponding concrete examples.

    Clearly I have not yet translated this abstraction:

    A deductive argument is said to be valid if and only if it takes a
    form such that its conclusion is a necessary consequence of all of its
    premises.

    Into a concrete example of the issue that it corrects, quite yet.

    *Here is my correction to that issue*
    A deductive argument is said to be valid if and only if it takes a >>>>>> form such that its conclusion is a necessary consequence of all of >>>>>> its premises.

    And that differs from the standard definition how exactly? Unless
    you have some special personal meaning for 'necessary consequence'
    it would

    Semantic relevance is a key aspect of 'necessary consequence'.

    Defined how exactly?

    André


    Here is the original way that semantic relevance was defined:
    Semantically unrelated premises and conclusion is not possible with
    syllogisms. https://en.wikipedia.org/wiki/Syllogism#Basic_structure

    Because syllogisms are comprised of
    https://en.wikipedia.org/wiki/Categorical_proposition





    My first thought is that if you are going to be limiting your reasoning capability to simple things. You seem to be stuck in using simple logic methods, which will limit what you can actually prove.


    Not when all of natural language semantics has been fully formalized and directly integrated into its own formal system.

    What you don't seem to understand is that much of what we have logically proven, is based on higher order logical systems, which these simple
    forms just can't handle.

    In particular, Computation theory, like much of mathematics, needs
    second order (or higher) logic forms, which the simple logic just can't handle.

    I created Minimal Type Theory to express HOL using very slightly adapted
    syntax of FOL. In an early version of MTT it translated its expressions
    into directed graphs so that pathological self-reference could be seen
    as infinite cycle in the di-graph.

    https://www.researchgate.net/publication/331859461_Minimal_Type_Theory_YACC_BNF

    --
    Copyright 2022 Pete Olcott

    "Talent hits a target no one else can hit;
    Genius hits a target no one else can see."
    Arthur Schopenhauer

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  • From Richard Damon@21:1/5 to olcott on Fri May 13 16:43:15 2022
    XPost: comp.theory, sci.logic, sci.lang.semantics

    On 5/13/22 3:43 PM, olcott wrote:
    On 5/13/2022 2:13 PM, Richard Damon wrote:
    On 5/13/22 2:10 PM, olcott wrote:
    On 5/13/2022 12:47 PM, Richard Damon wrote:
    On 5/13/22 1:20 PM, olcott wrote:
    *Validity and Soundness*
    A deductive argument is said to be valid if and only if it takes a
    form that makes it impossible for the premises to be true and the
    conclusion nevertheless to be false. Otherwise, a deductive
    argument is said to be invalid. https://iep.utm.edu/val-snd/

    If the Moon is made of green cheese then all dogs are cats is valid
    and even though premises and conclusion are semantically unrelated.

    *Here is my correction to that issue*
    A deductive argument is said to be valid if and only if it takes a
    form such that its conclusion is a necessary consequence of all of
    its premises.


    And, have you done the basic investigation to find out how much of
    conventional logic you invalidate with that change?


    It categorically changes everything that is broken.

    So, you are saying we need to throw out EVERYTHING we know and start
    over?


    Change everything that diverges from my spec:
    A deductive argument is said to be valid if and only if it takes a form
    such that its conclusion is a necessary consequence of all of its premises.

    I think, especially with the comment below, people will decide that
    your "new" logic systm isn't worth the cost to switch to.


    Note, that it may be hard to define "necessary consequence" in a
    formal matter.


    {A,B} ⊢ C only when truth preserving operations are applied to {A,B}
    to derive C.

    And what do you define truth perserving as?


    Semantic relevance is maintained.

    Normally the phrase means that True Premises always generate True
    Results (which means the statement "If the moon is made of green
    cheese then ll dogs are cats" IS Truth Preserving, since any time the
    premise is true (never) the conclusion is true.


    It should be noted that your example, while considered an vaild
    inference by normal logic, can never be used to actually prove its
    conclusion, so doesn't actually cause problems in normal logic (can
    you show a case where it does?)


    With my correction true and unprovable is impossible, unprovable
    simply means untrue.


    Ok, then you have just stated that your new logic system can't handle
    mathematics, and thus "Computer SCience" no longer exists as a logical
    system.


    It corrects the divergence of classical and symbolic logic from correct reasoning.

    This makes you system not much more than a toy for most people.

    Note, that at least by some meanings of your words, it could be
    construed that you only accept as a correct deductive argument, and
    arguement whose premises can at least some times be true, but there
    are some statements we don't know if they CAN be sometimes true, so
    your logic system would seem to not allow doing logic with that sort
    of statement.


    An analytic statement is only known to be true when it is derived by
    applying only truth preserving operations to all of its premises and
    all of its premises are known to be true, otherwise its truth value
    is unknown.


    KNOWN to be True, not IS TRUE.

    It remains unknown until it is known to be true or false.
    My system only eliminates impossibly true or false.


    So, you don't know what is still valid to use?



    Your statement even admits that truth value might be unknow, which
    might allow it to even be UNKNOWABLE (maybe just in that system) if it
    can't be proven or refuted.


    unprovable in the system means untrue in the system.

    And what does 'untrue' mean?

    We know that there is a number that solves an equation, but we don't
    know that number, or how to compute that number.

    Can we say that it is true that such a number exists?

    This means that we can define the floor of that number, which will be an integer (call it N), is it true that this number exists?

    That interger, MUST be either even or odd, so we know that either
    iseven(N) is true or isodd(N) is true.

    By your logic, the 'truth value' of both of those must be 'untrue' since
    we can not prove which one it is.

    This is the sort of problem you run into with your system.


    There is NOTHING about an analytic statement that says it can only be
    true if it is provable. Note, "its truth value is unknown" doesn't
    mean it doesn't have a truth value, just that we don't know what that
    value is.


    Within any formal system unprovable in the system means untrue in the
    system.

    The entire body of analytic truth is constructed only on the basis of semantic connections between expressions of language, or expressions
    that are stipulated to have the semantic property of Boolean true.
    Lacking both of these and the expression is untrue.

    Since axioms are provable on the basis that they are axioms then both of these factors that make an expression true also make it provable.


    You clearly are just stating words by rote and not actually
    understanding them.

    Analytic Truth is truth that is provable, that is correct, but it
    accepts that there is OTHER things that happen to be true but are not
    provable.

    You are making a Category Error in you logic system, and confusing
    Knowledge with Truth.



    You are confusing Knowledge with Truth.

    Your whole system is built on a Category Error.




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  • From Jeff Barnett@21:1/5 to Richard Damon on Fri May 13 14:44:23 2022
    XPost: comp.theory, sci.logic, sci.lang.semantics

    On 5/13/2022 11:47 AM, Richard Damon wrote:
    On 5/13/22 1:20 PM, olcott wrote:
    *Validity and Soundness*
    A deductive argument is said to be valid if and only if it takes a
    form that makes it impossible for the premises to be true and the
    conclusion nevertheless to be false. Otherwise, a deductive argument
    is said to be invalid. https://iep.utm.edu/val-snd/

    If the Moon is made of green cheese then all dogs are cats is valid
    and even though premises and conclusion are semantically unrelated.

    *Here is my correction to that issue*
    A deductive argument is said to be valid if and only if it takes a
    form such that its conclusion is a necessary consequence of all of its
    premises.


    And, have you done the basic investigation to find out how much of conventional logic you invalidate with that change?

    Note, that it may be hard to define "necessary consequence" in a formal matter.

    It should be noted that your example, while considered an vaild
    inference by normal logic, can never be used to actually prove its conclusion, so doesn't actually cause problems in normal logic (can you
    show a case where it does?)

    Most "heavy duty" theorem proving programs use resolution style logic
    and are beholding to the fact that "false -> anything" is valid. The
    standard approach is to reform the theorem so that you assume that the
    gives, axioms, whatever are true, and you assume the consequence (what
    the theorem says is true) is false. The conjunction of all this stuff (everything assumed connected with and operators) then processed. The
    general idea is then to show that this implies the empty conjunction: as
    we all know conjunction of an empty collection of clauses has truth
    value true (as intersection over an empty collection of sets is the
    universe of discourse). This in turn implies that deriving the empty conjunction contradicts the hypothesis as well as anything else in the
    domain of intercourse; and this actually means that the theorem is true
    and that it was just proven, i.e., if the theorem isn't true, the logic extended by including the theorem is inconsistent.

    Note that the quibble with the PO formulation is with the word "all" in
    the phrase "necessary consequence of all of its premises". In order to
    check this condition (consider brute force) you must PROVE the theorem
    false for every nonempty subset of the premises. This, must of course,
    include all the axioms as well as theorem specific assumptions. And just
    think of the consequences of that.

    Note, that at least by some meanings of your words, it could be
    construed that you only accept as a correct deductive argument, and
    arguement whose premises can at least some times be true, but there are
    some statements we don't know if they CAN be sometimes true, so your
    logic system would seem to not allow doing logic with that sort of statement.--
    Jeff Barnett

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  • From olcott@21:1/5 to Richard Damon on Fri May 13 15:56:11 2022
    XPost: comp.theory, sci.logic, sci.lang.semantics

    On 5/13/2022 3:43 PM, Richard Damon wrote:
    On 5/13/22 3:43 PM, olcott wrote:
    On 5/13/2022 2:13 PM, Richard Damon wrote:
    On 5/13/22 2:10 PM, olcott wrote:
    On 5/13/2022 12:47 PM, Richard Damon wrote:
    On 5/13/22 1:20 PM, olcott wrote:
    *Validity and Soundness*
    A deductive argument is said to be valid if and only if it takes a >>>>>> form that makes it impossible for the premises to be true and the
    conclusion nevertheless to be false. Otherwise, a deductive
    argument is said to be invalid. https://iep.utm.edu/val-snd/

    If the Moon is made of green cheese then all dogs are cats is
    valid and even though premises and conclusion are semantically
    unrelated.

    *Here is my correction to that issue*
    A deductive argument is said to be valid if and only if it takes a >>>>>> form such that its conclusion is a necessary consequence of all of >>>>>> its premises.


    And, have you done the basic investigation to find out how much of
    conventional logic you invalidate with that change?


    It categorically changes everything that is broken.

    So, you are saying we need to throw out EVERYTHING we know and start
    over?


    Change everything that diverges from my spec:
    A deductive argument is said to be valid if and only if it takes a
    form such that its conclusion is a necessary consequence of all of its
    premises.

    I think, especially with the comment below, people will decide that
    your "new" logic systm isn't worth the cost to switch to.


    Note, that it may be hard to define "necessary consequence" in a
    formal matter.


    {A,B} ⊢ C only when truth preserving operations are applied to {A,B} >>>> to derive C.

    And what do you define truth perserving as?


    Semantic relevance is maintained.

    Normally the phrase means that True Premises always generate True
    Results (which means the statement "If the moon is made of green
    cheese then ll dogs are cats" IS Truth Preserving, since any time the
    premise is true (never) the conclusion is true.


    It should be noted that your example, while considered an vaild
    inference by normal logic, can never be used to actually prove its
    conclusion, so doesn't actually cause problems in normal logic (can
    you show a case where it does?)


    With my correction true and unprovable is impossible, unprovable
    simply means untrue.


    Ok, then you have just stated that your new logic system can't handle
    mathematics, and thus "Computer SCience" no longer exists as a
    logical system.


    It corrects the divergence of classical and symbolic logic from
    correct reasoning.

    This makes you system not much more than a toy for most people.

    Note, that at least by some meanings of your words, it could be
    construed that you only accept as a correct deductive argument, and
    arguement whose premises can at least some times be true, but there
    are some statements we don't know if they CAN be sometimes true, so
    your logic system would seem to not allow doing logic with that
    sort of statement.


    An analytic statement is only known to be true when it is derived by
    applying only truth preserving operations to all of its premises and
    all of its premises are known to be true, otherwise its truth value
    is unknown.


    KNOWN to be True, not IS TRUE.

    It remains unknown until it is known to be true or false.
    My system only eliminates impossibly true or false.


    So, you don't know what is still valid to use?



    Your statement even admits that truth value might be unknow, which
    might allow it to even be UNKNOWABLE (maybe just in that system) if
    it can't be proven or refuted.


    unprovable in the system means untrue in the system.

    And what does 'untrue' mean?


    Untrue means the same thing as Prolog's negation as failure.

    We know that there is a number that solves an equation, but we don't
    know that number, or how to compute that number.

    Can we say that it is true that such a number exists?


    If you defined your terms correctly, then yes because this has been
    stipulated in your deinitions.

    This means that we can define the floor of that number, which will be an integer (call it N), is it true that this number exists?

    That interger, MUST be either even or odd, so we know that either
    iseven(N) is true or isodd(N) is true.

    By your logic, the 'truth value' of both of those must be 'untrue' since
    we can not prove which one it is.

    This is the sort of problem you run into with your system.


    There is NOTHING about an analytic statement that says it can only be
    true if it is provable. Note, "its truth value is unknown" doesn't
    mean it doesn't have a truth value, just that we don't know what that
    value is.


    Within any formal system unprovable in the system means untrue in the
    system.

    The entire body of analytic truth is constructed only on the basis of
    semantic connections between expressions of language, or expressions
    that are stipulated to have the semantic property of Boolean true.
    Lacking both of these and the expression is untrue.

    Since axioms are provable on the basis that they are axioms then both
    of these factors that make an expression true also make it provable.


    You clearly are just stating words by rote and not actually
    understanding them.


    There are only two possible ways that any analytical expression of
    language can possibly be true:
    (1) It is stipulated to be true.
    (2) It is derived by applying only truth preserving operations to (1) or
    the consequences of (2).

    Analytic Truth is truth that is provable, that is correct, but it
    accepts that there is OTHER things that happen to be true but are not provable.


    Analytic truth includes every expression of language that can be
    completely verified as totally true entirely on the basis of its meaning without requiring any sense data from the sense organs.

    Empirical expressions of language also require sense data from the sense
    organs to verify their truth.

    You are making a Category Error in you logic system, and confusing
    Knowledge with Truth.



    You are confusing Knowledge with Truth.

    Your whole system is built on a Category Error.






    --
    Copyright 2022 Pete Olcott

    "Talent hits a target no one else can hit;
    Genius hits a target no one else can see."
    Arthur Schopenhauer

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Richard Damon@21:1/5 to olcott on Fri May 13 17:30:57 2022
    XPost: comp.theory, sci.logic, sci.lang.semantics

    On 5/13/22 4:56 PM, olcott wrote:
    On 5/13/2022 3:43 PM, Richard Damon wrote:
    On 5/13/22 3:43 PM, olcott wrote:
    On 5/13/2022 2:13 PM, Richard Damon wrote:
    On 5/13/22 2:10 PM, olcott wrote:
    On 5/13/2022 12:47 PM, Richard Damon wrote:
    On 5/13/22 1:20 PM, olcott wrote:
    *Validity and Soundness*
    A deductive argument is said to be valid if and only if it takes >>>>>>> a form that makes it impossible for the premises to be true and
    the conclusion nevertheless to be false. Otherwise, a deductive
    argument is said to be invalid. https://iep.utm.edu/val-snd/

    If the Moon is made of green cheese then all dogs are cats is
    valid and even though premises and conclusion are semantically
    unrelated.

    *Here is my correction to that issue*
    A deductive argument is said to be valid if and only if it takes >>>>>>> a form such that its conclusion is a necessary consequence of all >>>>>>> of its premises.


    And, have you done the basic investigation to find out how much of >>>>>> conventional logic you invalidate with that change?


    It categorically changes everything that is broken.

    So, you are saying we need to throw out EVERYTHING we know and start
    over?


    Change everything that diverges from my spec:
    A deductive argument is said to be valid if and only if it takes a
    form such that its conclusion is a necessary consequence of all of
    its premises.

    I think, especially with the comment below, people will decide that
    your "new" logic systm isn't worth the cost to switch to.


    Note, that it may be hard to define "necessary consequence" in a
    formal matter.


    {A,B} ⊢ C only when truth preserving operations are applied to
    {A,B} to derive C.

    And what do you define truth perserving as?


    Semantic relevance is maintained.

    Normally the phrase means that True Premises always generate True
    Results (which means the statement "If the moon is made of green
    cheese then ll dogs are cats" IS Truth Preserving, since any time
    the premise is true (never) the conclusion is true.


    It should be noted that your example, while considered an vaild
    inference by normal logic, can never be used to actually prove its >>>>>> conclusion, so doesn't actually cause problems in normal logic
    (can you show a case where it does?)


    With my correction true and unprovable is impossible, unprovable
    simply means untrue.


    Ok, then you have just stated that your new logic system can't
    handle mathematics, and thus "Computer SCience" no longer exists as
    a logical system.


    It corrects the divergence of classical and symbolic logic from
    correct reasoning.

    This makes you system not much more than a toy for most people.

    Note, that at least by some meanings of your words, it could be
    construed that you only accept as a correct deductive argument,
    and arguement whose premises can at least some times be true, but
    there are some statements we don't know if they CAN be sometimes
    true, so your logic system would seem to not allow doing logic
    with that sort of statement.


    An analytic statement is only known to be true when it is derived
    by applying only truth preserving operations to all of its premises
    and all of its premises are known to be true, otherwise its truth
    value is unknown.


    KNOWN to be True, not IS TRUE.

    It remains unknown until it is known to be true or false.
    My system only eliminates impossibly true or false.


    So, you don't know what is still valid to use?



    Your statement even admits that truth value might be unknow, which
    might allow it to even be UNKNOWABLE (maybe just in that system) if
    it can't be proven or refuted.


    unprovable in the system means untrue in the system.

    And what does 'untrue' mean?


    Untrue means the same thing as Prolog's negation as failure.

    Which means... ?

    Prolog, as I remember, ASSUMES that anything not provable is FALSE (not 'untrue').


    We know that there is a number that solves an equation, but we don't
    know that number, or how to compute that number.

    Can we say that it is true that such a number exists?


    If you defined your terms correctly, then yes because this has been stipulated in your deinitions.

    This means that we can define the floor of that number, which will be
    an integer (call it N), is it true that this number exists?

    That interger, MUST be either even or odd, so we know that either
    iseven(N) is true or isodd(N) is true.

    By your logic, the 'truth value' of both of those must be 'untrue'
    since we can not prove which one it is.

    This is the sort of problem you run into with your system.


    There is NOTHING about an analytic statement that says it can only
    be true if it is provable. Note, "its truth value is unknown"
    doesn't mean it doesn't have a truth value, just that we don't know
    what that value is.


    Within any formal system unprovable in the system means untrue in the
    system.

    The entire body of analytic truth is constructed only on the basis of
    semantic connections between expressions of language, or expressions
    that are stipulated to have the semantic property of Boolean true.
    Lacking both of these and the expression is untrue.

    Since axioms are provable on the basis that they are axioms then both
    of these factors that make an expression true also make it provable.


    You clearly are just stating words by rote and not actually
    understanding them.


    There are only two possible ways that any analytical expression of
    language can possibly be true:
    (1) It is stipulated to be true.
    (2) It is derived by applying only truth preserving operations to (1) or
    the consequences of (2).

    So there exists an integer number N is neither Even or Odd? (it is
    untrue for both tests)

    I don't think you actually understand what that means.


    Analytic Truth is truth that is provable, that is correct, but it
    accepts that there is OTHER things that happen to be true but are not
    provable.


    Analytic truth includes every expression of language that can be
    completely verified as totally true entirely on the basis of its meaning without requiring any sense data from the sense organs.

    Empirical expressions of language also require sense data from the sense organs to verify their truth.

    You still don't understand, do you.

    You still confuse Truth with Knowledge.

    Pitiful.


    You are making a Category Error in you logic system, and confusing
    Knowledge with Truth.



    You are confusing Knowledge with Truth.

    Your whole system is built on a Category Error.







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  • From Richard Damon@21:1/5 to olcott on Fri May 13 17:39:35 2022
    XPost: comp.theory, sci.logic, sci.lang.semantics

    On 5/13/22 4:14 PM, olcott wrote:
    On 5/13/2022 3:03 PM, Richard Damon wrote:
    On 5/13/22 3:11 PM, olcott wrote:
    On 5/13/2022 2:00 PM, André G. Isaak wrote:
    On 2022-05-13 12:50, olcott wrote:
    On 5/13/2022 1:28 PM, André G. Isaak wrote:
    On 2022-05-13 11:20, olcott wrote:
    *Validity and Soundness*
    A deductive argument is said to be valid if and only if it takes >>>>>>> a form that makes it impossible for the premises to be true and
    the conclusion nevertheless to be false. Otherwise, a deductive
    argument is said to be invalid. https://iep.utm.edu/val-snd/

    If the Moon is made of green cheese then all dogs are cats is
    valid and even though premises and conclusion are semantically
    unrelated.

    That isn't valid. Perhaps you should learn what 'valid' actually
    means before you attempt to "correct" the definition.

    [Also, the above isn't even an argument. It is simply a
    conditional statement. It has no conclusion].


    (a) The Moon is made of green cheese.
    (b) Water is a kind of concrete.
    (c) Therefore all dogs are cats.

    Because the premises are false and the conclusion is false it is
    not a case of the conclusion is true and the premises are false,
    thus meets the above validity criteria.

    No. It isn't valid. You don't seem to grasp the concept of validity.

    Logic has no concept of whether, for example, the moon is made of
    green cheese. An argument is valid if there is no truth *assignment*
    under which the premises are true and the conclusion is false. The
    actual truth values of these expressions don't play a role in the
    definition of validity.


    I reach my key insights by progressively refining very high level
    abstractions into their corresponding concrete examples.

    Clearly I have not yet translated this abstraction:

    A deductive argument is said to be valid if and only if it takes a
    form such that its conclusion is a necessary consequence of all of
    its premises.

    Into a concrete example of the issue that it corrects, quite yet.

    *Here is my correction to that issue*
    A deductive argument is said to be valid if and only if it takes >>>>>>> a form such that its conclusion is a necessary consequence of all >>>>>>> of its premises.

    And that differs from the standard definition how exactly? Unless
    you have some special personal meaning for 'necessary consequence' >>>>>> it would

    Semantic relevance is a key aspect of 'necessary consequence'.

    Defined how exactly?

    André


    Here is the original way that semantic relevance was defined:
    Semantically unrelated premises and conclusion is not possible with
    syllogisms. https://en.wikipedia.org/wiki/Syllogism#Basic_structure

    Because syllogisms are comprised of
    https://en.wikipedia.org/wiki/Categorical_proposition





    My first thought is that if you are going to be limiting your
    reasoning capability to simple things. You seem to be stuck in using
    simple logic methods, which will limit what you can actually prove.


    Not when all of natural language semantics has been fully formalized and directly integrated into its own formal system.

    Nope doesn't work. Remember, formal system are based on a finite, or
    perhaps extended to countable, number of base axiom.

    I think you basis is going to hit the problem that the number of natural language 'facts' you are entering into your system isn't so limited.

    Having an uncountable number of axioms in your system breaks a lot of
    thngs. In fact, I think it breaks the definition of 'provable' or
    'refutable'.


    What you don't seem to understand is that much of what we have
    logically proven, is based on higher order logical systems, which
    these simple forms just can't handle.

    In particular, Computation theory, like much of mathematics, needs
    second order (or higher) logic forms, which the simple logic just
    can't handle.

    I created Minimal Type Theory to express HOL using very slightly adapted syntax of FOL. In an early version of MTT it translated its expressions
    into directed graphs so that pathological self-reference could be seen
    as infinite cycle in the di-graph.

    https://www.researchgate.net/publication/331859461_Minimal_Type_Theory_YACC_BNF


    Again, the error you are going to run into is your system is now based
    on an uncountable number of inital truths, so a lot of the rules for
    reasoning break down. This makes you system VERY prone to becoming
    inconsistent (if not a certainty).

    There are problems when you allow uncountable infinites into your base
    logic.

    --- SoupGate-Win32 v1.05
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  • From olcott@21:1/5 to Richard Damon on Fri May 13 16:53:48 2022
    XPost: comp.theory, sci.logic, sci.lang.semantics

    On 5/13/2022 4:30 PM, Richard Damon wrote:
    On 5/13/22 4:56 PM, olcott wrote:
    On 5/13/2022 3:43 PM, Richard Damon wrote:
    On 5/13/22 3:43 PM, olcott wrote:
    On 5/13/2022 2:13 PM, Richard Damon wrote:
    On 5/13/22 2:10 PM, olcott wrote:
    On 5/13/2022 12:47 PM, Richard Damon wrote:
    On 5/13/22 1:20 PM, olcott wrote:
    *Validity and Soundness*
    A deductive argument is said to be valid if and only if it takes >>>>>>>> a form that makes it impossible for the premises to be true and >>>>>>>> the conclusion nevertheless to be false. Otherwise, a deductive >>>>>>>> argument is said to be invalid. https://iep.utm.edu/val-snd/

    If the Moon is made of green cheese then all dogs are cats is
    valid and even though premises and conclusion are semantically >>>>>>>> unrelated.

    *Here is my correction to that issue*
    A deductive argument is said to be valid if and only if it takes >>>>>>>> a form such that its conclusion is a necessary consequence of
    all of its premises.


    And, have you done the basic investigation to find out how much
    of conventional logic you invalidate with that change?


    It categorically changes everything that is broken.

    So, you are saying we need to throw out EVERYTHING we know and
    start over?


    Change everything that diverges from my spec:
    A deductive argument is said to be valid if and only if it takes a
    form such that its conclusion is a necessary consequence of all of
    its premises.

    I think, especially with the comment below, people will decide that
    your "new" logic systm isn't worth the cost to switch to.


    Note, that it may be hard to define "necessary consequence" in a >>>>>>> formal matter.


    {A,B} ⊢ C only when truth preserving operations are applied to
    {A,B} to derive C.

    And what do you define truth perserving as?


    Semantic relevance is maintained.

    Normally the phrase means that True Premises always generate True
    Results (which means the statement "If the moon is made of green
    cheese then ll dogs are cats" IS Truth Preserving, since any time
    the premise is true (never) the conclusion is true.


    It should be noted that your example, while considered an vaild
    inference by normal logic, can never be used to actually prove
    its conclusion, so doesn't actually cause problems in normal
    logic (can you show a case where it does?)


    With my correction true and unprovable is impossible, unprovable
    simply means untrue.


    Ok, then you have just stated that your new logic system can't
    handle mathematics, and thus "Computer SCience" no longer exists as
    a logical system.


    It corrects the divergence of classical and symbolic logic from
    correct reasoning.

    This makes you system not much more than a toy for most people.

    Note, that at least by some meanings of your words, it could be
    construed that you only accept as a correct deductive argument,
    and arguement whose premises can at least some times be true, but >>>>>>> there are some statements we don't know if they CAN be sometimes >>>>>>> true, so your logic system would seem to not allow doing logic
    with that sort of statement.


    An analytic statement is only known to be true when it is derived
    by applying only truth preserving operations to all of its
    premises and all of its premises are known to be true, otherwise
    its truth value is unknown.


    KNOWN to be True, not IS TRUE.

    It remains unknown until it is known to be true or false.
    My system only eliminates impossibly true or false.


    So, you don't know what is still valid to use?



    Your statement even admits that truth value might be unknow, which
    might allow it to even be UNKNOWABLE (maybe just in that system) if
    it can't be proven or refuted.


    unprovable in the system means untrue in the system.

    And what does 'untrue' mean?


    Untrue means the same thing as Prolog's negation as failure.

    Which means... ?

    Prolog, as I remember, ASSUMES that anything not provable is FALSE (not 'untrue').


    Unprovable means untrue and does not mean false in Prolog.


    We know that there is a number that solves an equation, but we don't
    know that number, or how to compute that number.

    Can we say that it is true that such a number exists?


    If you defined your terms correctly, then yes because this has been
    stipulated in your deinitions.

    This means that we can define the floor of that number, which will be
    an integer (call it N), is it true that this number exists?

    That interger, MUST be either even or odd, so we know that either
    iseven(N) is true or isodd(N) is true.

    By your logic, the 'truth value' of both of those must be 'untrue'
    since we can not prove which one it is.

    This is the sort of problem you run into with your system.


    There is NOTHING about an analytic statement that says it can only
    be true if it is provable. Note, "its truth value is unknown"
    doesn't mean it doesn't have a truth value, just that we don't know
    what that value is.


    Within any formal system unprovable in the system means untrue in
    the system.

    The entire body of analytic truth is constructed only on the basis
    of semantic connections between expressions of language, or
    expressions that are stipulated to have the semantic property of
    Boolean true. Lacking both of these and the expression is untrue.

    Since axioms are provable on the basis that they are axioms then
    both of these factors that make an expression true also make it
    provable.


    You clearly are just stating words by rote and not actually
    understanding them.


    There are only two possible ways that any analytical expression of
    language can possibly be true:
    (1) It is stipulated to be true.
    (2) It is derived by applying only truth preserving operations to (1)
    or the consequences of (2).

    So there exists an integer number N is neither Even or Odd? (it is
    untrue for both tests)

    I don't think you actually understand what that means.


    Analytic Truth is truth that is provable, that is correct, but it
    accepts that there is OTHER things that happen to be true but are not
    provable.


    Analytic truth includes every expression of language that can be
    completely verified as totally true entirely on the basis of its
    meaning without requiring any sense data from the sense organs.

    Empirical expressions of language also require sense data from the
    sense organs to verify their truth.

    You still don't understand, do you.

    You still confuse Truth with Knowledge.
    There are only two possible ways that any analytical expression of
    language can possibly be true:
    (1) It is stipulated to be true.
    (2) It is derived by applying only truth preserving operations to (1)
    or the consequences of (2).

    Try and provide an example of a possible truth that does not require one
    of those two.


    --
    Copyright 2022 Pete Olcott

    "Talent hits a target no one else can hit;
    Genius hits a target no one else can see."
    Arthur Schopenhauer

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  • From Richard Damon@21:1/5 to olcott on Fri May 13 17:56:05 2022
    XPost: comp.theory, sci.logic, sci.lang.semantics

    On 5/13/22 4:08 PM, olcott wrote:

    True and unprovable become impossible because Provable() is an aspect of True().


    Can you actually PROVE that statement, if not, by its own defintion, it
    isn't True.

    If you resort to making it an axiom, then you run into the issue that
    the accepted axioms define the system, and don't apply to systems that
    don't take those axioms.

    You also need to be sure that you don't make your system inconsistent,
    and there exists proofs that show that such an axiom lead to
    inconsistent systems once they try to take on certail levels of complexity.

    In particular, no logic system can express all the properties of the
    integer number system and be consistent (no provable statement can be
    refuted) and complete (all truths are provable) at the same time.

    Basically, you are defining youself into a corner and restricting what
    you can meaningfully logically deduce.

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  • From olcott@21:1/5 to Richard Damon on Fri May 13 16:56:26 2022
    XPost: comp.theory, sci.logic, sci.lang.semantics

    On 5/13/2022 4:39 PM, Richard Damon wrote:
    On 5/13/22 4:14 PM, olcott wrote:
    On 5/13/2022 3:03 PM, Richard Damon wrote:
    On 5/13/22 3:11 PM, olcott wrote:
    On 5/13/2022 2:00 PM, André G. Isaak wrote:
    On 2022-05-13 12:50, olcott wrote:
    On 5/13/2022 1:28 PM, André G. Isaak wrote:
    On 2022-05-13 11:20, olcott wrote:
    *Validity and Soundness*
    A deductive argument is said to be valid if and only if it takes >>>>>>>> a form that makes it impossible for the premises to be true and >>>>>>>> the conclusion nevertheless to be false. Otherwise, a deductive >>>>>>>> argument is said to be invalid. https://iep.utm.edu/val-snd/

    If the Moon is made of green cheese then all dogs are cats is
    valid and even though premises and conclusion are semantically >>>>>>>> unrelated.

    That isn't valid. Perhaps you should learn what 'valid' actually >>>>>>> means before you attempt to "correct" the definition.

    [Also, the above isn't even an argument. It is simply a
    conditional statement. It has no conclusion].


    (a) The Moon is made of green cheese.
    (b) Water is a kind of concrete.
    (c) Therefore all dogs are cats.

    Because the premises are false and the conclusion is false it is
    not a case of the conclusion is true and the premises are false,
    thus meets the above validity criteria.

    No. It isn't valid. You don't seem to grasp the concept of validity. >>>>>
    Logic has no concept of whether, for example, the moon is made of
    green cheese. An argument is valid if there is no truth
    *assignment* under which the premises are true and the conclusion
    is false. The actual truth values of these expressions don't play a
    role in the definition of validity.


    I reach my key insights by progressively refining very high level
    abstractions into their corresponding concrete examples.

    Clearly I have not yet translated this abstraction:

    A deductive argument is said to be valid if and only if it takes a
    form such that its conclusion is a necessary consequence of all of
    its premises.

    Into a concrete example of the issue that it corrects, quite yet.

    *Here is my correction to that issue*
    A deductive argument is said to be valid if and only if it takes >>>>>>>> a form such that its conclusion is a necessary consequence of
    all of its premises.

    And that differs from the standard definition how exactly? Unless >>>>>>> you have some special personal meaning for 'necessary
    consequence' it would

    Semantic relevance is a key aspect of 'necessary consequence'.

    Defined how exactly?

    André


    Here is the original way that semantic relevance was defined:
    Semantically unrelated premises and conclusion is not possible with
    syllogisms. https://en.wikipedia.org/wiki/Syllogism#Basic_structure

    Because syllogisms are comprised of
    https://en.wikipedia.org/wiki/Categorical_proposition





    My first thought is that if you are going to be limiting your
    reasoning capability to simple things. You seem to be stuck in using
    simple logic methods, which will limit what you can actually prove.


    Not when all of natural language semantics has been fully formalized
    and directly integrated into its own formal system.

    Nope doesn't work. Remember, formal system are based on a finite, or
    perhaps extended to countable, number of base axiom.

    I think you basis is going to hit the problem that the number of natural language 'facts' you are entering into your system isn't so limited.

    Having an uncountable number of axioms in your system breaks a lot of
    thngs. In fact, I think it breaks the definition of 'provable' or 'refutable'.


    What you don't seem to understand is that much of what we have
    logically proven, is based on higher order logical systems, which
    these simple forms just can't handle.

    In particular, Computation theory, like much of mathematics, needs
    second order (or higher) logic forms, which the simple logic just
    can't handle.

    I created Minimal Type Theory to express HOL using very slightly
    adapted syntax of FOL. In an early version of MTT it translated its
    expressions into directed graphs so that pathological self-reference
    could be seen as infinite cycle in the di-graph.

    https://www.researchgate.net/publication/331859461_Minimal_Type_Theory_YACC_BNF


    Again, the error you are going to run into is your system is now based
    on an uncountable number of inital truths, so a lot of the rules for reasoning break down. This makes you system VERY prone to becoming inconsistent (if not a certainty).

    There are problems when you allow uncountable infinites into your base
    logic.


    Uncountable truths that are entirely comprised of different combinations
    of countable constituent parts are evaluatable on the basis of these constituents that are later recombined back into the original expression.

    --
    Copyright 2022 Pete Olcott

    "Talent hits a target no one else can hit;
    Genius hits a target no one else can see."
    Arthur Schopenhauer

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Richard Damon@21:1/5 to olcott on Fri May 13 18:14:53 2022
    XPost: comp.theory, sci.logic, sci.lang.semantics

    On 5/13/22 5:53 PM, olcott wrote:
    On 5/13/2022 4:30 PM, Richard Damon wrote:
    On 5/13/22 4:56 PM, olcott wrote:
    On 5/13/2022 3:43 PM, Richard Damon wrote:
    On 5/13/22 3:43 PM, olcott wrote:
    On 5/13/2022 2:13 PM, Richard Damon wrote:
    On 5/13/22 2:10 PM, olcott wrote:
    On 5/13/2022 12:47 PM, Richard Damon wrote:
    On 5/13/22 1:20 PM, olcott wrote:
    *Validity and Soundness*
    A deductive argument is said to be valid if and only if it
    takes a form that makes it impossible for the premises to be >>>>>>>>> true and the conclusion nevertheless to be false. Otherwise, a >>>>>>>>> deductive argument is said to be invalid.
    https://iep.utm.edu/val-snd/

    If the Moon is made of green cheese then all dogs are cats is >>>>>>>>> valid and even though premises and conclusion are semantically >>>>>>>>> unrelated.

    *Here is my correction to that issue*
    A deductive argument is said to be valid if and only if it
    takes a form such that its conclusion is a necessary
    consequence of all of its premises.


    And, have you done the basic investigation to find out how much >>>>>>>> of conventional logic you invalidate with that change?


    It categorically changes everything that is broken.

    So, you are saying we need to throw out EVERYTHING we know and
    start over?


    Change everything that diverges from my spec:
    A deductive argument is said to be valid if and only if it takes a
    form such that its conclusion is a necessary consequence of all of
    its premises.

    I think, especially with the comment below, people will decide
    that your "new" logic systm isn't worth the cost to switch to.


    Note, that it may be hard to define "necessary consequence" in a >>>>>>>> formal matter.


    {A,B} ⊢ C only when truth preserving operations are applied to >>>>>>> {A,B} to derive C.

    And what do you define truth perserving as?


    Semantic relevance is maintained.

    Normally the phrase means that True Premises always generate True
    Results (which means the statement "If the moon is made of green
    cheese then ll dogs are cats" IS Truth Preserving, since any time
    the premise is true (never) the conclusion is true.


    It should be noted that your example, while considered an vaild >>>>>>>> inference by normal logic, can never be used to actually prove >>>>>>>> its conclusion, so doesn't actually cause problems in normal
    logic (can you show a case where it does?)


    With my correction true and unprovable is impossible, unprovable >>>>>>> simply means untrue.


    Ok, then you have just stated that your new logic system can't
    handle mathematics, and thus "Computer SCience" no longer exists
    as a logical system.


    It corrects the divergence of classical and symbolic logic from
    correct reasoning.

    This makes you system not much more than a toy for most people.

    Note, that at least by some meanings of your words, it could be >>>>>>>> construed that you only accept as a correct deductive argument, >>>>>>>> and arguement whose premises can at least some times be true,
    but there are some statements we don't know if they CAN be
    sometimes true, so your logic system would seem to not allow
    doing logic with that sort of statement.


    An analytic statement is only known to be true when it is derived >>>>>>> by applying only truth preserving operations to all of its
    premises and all of its premises are known to be true, otherwise >>>>>>> its truth value is unknown.


    KNOWN to be True, not IS TRUE.

    It remains unknown until it is known to be true or false.
    My system only eliminates impossibly true or false.


    So, you don't know what is still valid to use?



    Your statement even admits that truth value might be unknow, which >>>>>> might allow it to even be UNKNOWABLE (maybe just in that system)
    if it can't be proven or refuted.


    unprovable in the system means untrue in the system.

    And what does 'untrue' mean?


    Untrue means the same thing as Prolog's negation as failure.

    Which means... ?

    Prolog, as I remember, ASSUMES that anything not provable is FALSE
    (not 'untrue').


    Unprovable means untrue and does not mean false in Prolog.


    We know that there is a number that solves an equation, but we don't
    know that number, or how to compute that number.

    Can we say that it is true that such a number exists?


    If you defined your terms correctly, then yes because this has been
    stipulated in your deinitions.

    This means that we can define the floor of that number, which will
    be an integer (call it N), is it true that this number exists?

    That interger, MUST be either even or odd, so we know that either
    iseven(N) is true or isodd(N) is true.

    By your logic, the 'truth value' of both of those must be 'untrue'
    since we can not prove which one it is.

    This is the sort of problem you run into with your system.


    There is NOTHING about an analytic statement that says it can only >>>>>> be true if it is provable. Note, "its truth value is unknown"
    doesn't mean it doesn't have a truth value, just that we don't
    know what that value is.


    Within any formal system unprovable in the system means untrue in
    the system.

    The entire body of analytic truth is constructed only on the basis
    of semantic connections between expressions of language, or
    expressions that are stipulated to have the semantic property of
    Boolean true. Lacking both of these and the expression is untrue.

    Since axioms are provable on the basis that they are axioms then
    both of these factors that make an expression true also make it
    provable.


    You clearly are just stating words by rote and not actually
    understanding them.


    There are only two possible ways that any analytical expression of
    language can possibly be true:
    (1) It is stipulated to be true.
    (2) It is derived by applying only truth preserving operations to (1)
    or the consequences of (2).

    So there exists an integer number N is neither Even or Odd? (it is
    untrue for both tests)

    I don't think you actually understand what that means.


    Analytic Truth is truth that is provable, that is correct, but it
    accepts that there is OTHER things that happen to be true but are
    not provable.


    Analytic truth includes every expression of language that can be
    completely verified as totally true entirely on the basis of its
    meaning without requiring any sense data from the sense organs.

    Empirical expressions of language also require sense data from the
    sense organs to verify their truth.

    You still don't understand, do you.

    You still confuse Truth with Knowledge.
    There are only two possible ways that any analytical expression of
    language can possibly be true:
    (1) It is stipulated to be true.
    (2) It is derived by applying only truth preserving operations to (1)
    or the consequences of (2).

    Try and provide an example of a possible truth that does not require one
    of those two.


    The result of applying the operation of replacing N by N/2 if N is even
    or by 3N+1 if N is odd will eventually get you to the number 1 for all
    Natural numbers N > 0.

    This statement MUST be either True or False, by its nature, there is no
    other possible state.

    This statement seems to be true, but it has unable to be proven to be true.

    Yes, we can not validly USE the idea that this statement is true to
    prove something else, because we know that it is still possible that it
    won't be true. But we CAN use that it will either be true or false to
    show something.

    That is an analytical expression that isn't proven to be an analytical
    truth, but it may still be true, and is neither stipulated true or
    derived from an analytical proof.

    Again. you are confusing True, with Proven/Known.

    It MAY be True, or its Converse IS True, we know it must be one or the
    other.

    It is not KNOWN to be True, or Proven.

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Richard Damon@21:1/5 to olcott on Fri May 13 18:19:08 2022
    XPost: comp.theory, sci.logic, sci.lang.semantics

    On 5/13/22 5:56 PM, olcott wrote:
    On 5/13/2022 4:39 PM, Richard Damon wrote:
    On 5/13/22 4:14 PM, olcott wrote:
    On 5/13/2022 3:03 PM, Richard Damon wrote:
    On 5/13/22 3:11 PM, olcott wrote:
    On 5/13/2022 2:00 PM, André G. Isaak wrote:
    On 2022-05-13 12:50, olcott wrote:
    On 5/13/2022 1:28 PM, André G. Isaak wrote:
    On 2022-05-13 11:20, olcott wrote:
    *Validity and Soundness*
    A deductive argument is said to be valid if and only if it
    takes a form that makes it impossible for the premises to be >>>>>>>>> true and the conclusion nevertheless to be false. Otherwise, a >>>>>>>>> deductive argument is said to be invalid.
    https://iep.utm.edu/val-snd/

    If the Moon is made of green cheese then all dogs are cats is >>>>>>>>> valid and even though premises and conclusion are semantically >>>>>>>>> unrelated.

    That isn't valid. Perhaps you should learn what 'valid' actually >>>>>>>> means before you attempt to "correct" the definition.

    [Also, the above isn't even an argument. It is simply a
    conditional statement. It has no conclusion].


    (a) The Moon is made of green cheese.
    (b) Water is a kind of concrete.
    (c) Therefore all dogs are cats.

    Because the premises are false and the conclusion is false it is >>>>>>> not a case of the conclusion is true and the premises are false, >>>>>>> thus meets the above validity criteria.

    No. It isn't valid. You don't seem to grasp the concept of validity. >>>>>>
    Logic has no concept of whether, for example, the moon is made of
    green cheese. An argument is valid if there is no truth
    *assignment* under which the premises are true and the conclusion
    is false. The actual truth values of these expressions don't play
    a role in the definition of validity.


    I reach my key insights by progressively refining very high level
    abstractions into their corresponding concrete examples.

    Clearly I have not yet translated this abstraction:

    A deductive argument is said to be valid if and only if it takes a
    form such that its conclusion is a necessary consequence of all of
    its premises.

    Into a concrete example of the issue that it corrects, quite yet.

    *Here is my correction to that issue*
    A deductive argument is said to be valid if and only if it
    takes a form such that its conclusion is a necessary
    consequence of all of its premises.

    And that differs from the standard definition how exactly?
    Unless you have some special personal meaning for 'necessary
    consequence' it would

    Semantic relevance is a key aspect of 'necessary consequence'.

    Defined how exactly?

    André


    Here is the original way that semantic relevance was defined:
    Semantically unrelated premises and conclusion is not possible with
    syllogisms. https://en.wikipedia.org/wiki/Syllogism#Basic_structure

    Because syllogisms are comprised of
    https://en.wikipedia.org/wiki/Categorical_proposition





    My first thought is that if you are going to be limiting your
    reasoning capability to simple things. You seem to be stuck in using
    simple logic methods, which will limit what you can actually prove.


    Not when all of natural language semantics has been fully formalized
    and directly integrated into its own formal system.

    Nope doesn't work. Remember, formal system are based on a finite, or
    perhaps extended to countable, number of base axiom.

    I think you basis is going to hit the problem that the number of
    natural language 'facts' you are entering into your system isn't so
    limited.

    Having an uncountable number of axioms in your system breaks a lot of
    thngs. In fact, I think it breaks the definition of 'provable' or
    'refutable'.


    What you don't seem to understand is that much of what we have
    logically proven, is based on higher order logical systems, which
    these simple forms just can't handle.

    In particular, Computation theory, like much of mathematics, needs
    second order (or higher) logic forms, which the simple logic just
    can't handle.

    I created Minimal Type Theory to express HOL using very slightly
    adapted syntax of FOL. In an early version of MTT it translated its
    expressions into directed graphs so that pathological self-reference
    could be seen as infinite cycle in the di-graph.

    https://www.researchgate.net/publication/331859461_Minimal_Type_Theory_YACC_BNF


    Again, the error you are going to run into is your system is now based
    on an uncountable number of inital truths, so a lot of the rules for
    reasoning break down. This makes you system VERY prone to becoming
    inconsistent (if not a certainty).

    There are problems when you allow uncountable infinites into your base
    logic.


    Uncountable truths that are entirely comprised of different combinations
    of countable constituent parts are evaluatable on the basis of these constituents that are later recombined back into the original expression.


    Nope, if you can create an uncountable number of combinations, you CAN'T
    just use the countable number of base elements.

    Proving is based on creating a FINITE (or countable) sequence of steps
    that combine a FINITE (or countable0 number of proven statements to show something.

    If the logic system can create an uncountable number of true statements
    to work from, then there may be an sequence from an UNCOUNATBLE number
    of steps fromt the countble base set, and thus beyond the reach of proving.

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From olcott@21:1/5 to Richard Damon on Fri May 13 17:23:59 2022
    XPost: comp.theory, sci.logic, sci.lang.semantics

    On 5/13/2022 5:14 PM, Richard Damon wrote:
    On 5/13/22 5:53 PM, olcott wrote:
    On 5/13/2022 4:30 PM, Richard Damon wrote:
    On 5/13/22 4:56 PM, olcott wrote:
    On 5/13/2022 3:43 PM, Richard Damon wrote:
    On 5/13/22 3:43 PM, olcott wrote:
    On 5/13/2022 2:13 PM, Richard Damon wrote:
    On 5/13/22 2:10 PM, olcott wrote:
    On 5/13/2022 12:47 PM, Richard Damon wrote:
    On 5/13/22 1:20 PM, olcott wrote:
    *Validity and Soundness*
    A deductive argument is said to be valid if and only if it >>>>>>>>>> takes a form that makes it impossible for the premises to be >>>>>>>>>> true and the conclusion nevertheless to be false. Otherwise, a >>>>>>>>>> deductive argument is said to be invalid.
    https://iep.utm.edu/val-snd/

    If the Moon is made of green cheese then all dogs are cats is >>>>>>>>>> valid and even though premises and conclusion are semantically >>>>>>>>>> unrelated.

    *Here is my correction to that issue*
    A deductive argument is said to be valid if and only if it >>>>>>>>>> takes a form such that its conclusion is a necessary
    consequence of all of its premises.


    And, have you done the basic investigation to find out how much >>>>>>>>> of conventional logic you invalidate with that change?


    It categorically changes everything that is broken.

    So, you are saying we need to throw out EVERYTHING we know and
    start over?


    Change everything that diverges from my spec:
    A deductive argument is said to be valid if and only if it takes a >>>>>> form such that its conclusion is a necessary consequence of all of >>>>>> its premises.

    I think, especially with the comment below, people will decide
    that your "new" logic systm isn't worth the cost to switch to.


    Note, that it may be hard to define "necessary consequence" in >>>>>>>>> a formal matter.


    {A,B} ⊢ C only when truth preserving operations are applied to >>>>>>>> {A,B} to derive C.

    And what do you define truth perserving as?


    Semantic relevance is maintained.

    Normally the phrase means that True Premises always generate True >>>>>>> Results (which means the statement "If the moon is made of green >>>>>>> cheese then ll dogs are cats" IS Truth Preserving, since any time >>>>>>> the premise is true (never) the conclusion is true.


    It should be noted that your example, while considered an vaild >>>>>>>>> inference by normal logic, can never be used to actually prove >>>>>>>>> its conclusion, so doesn't actually cause problems in normal >>>>>>>>> logic (can you show a case where it does?)


    With my correction true and unprovable is impossible, unprovable >>>>>>>> simply means untrue.


    Ok, then you have just stated that your new logic system can't
    handle mathematics, and thus "Computer SCience" no longer exists >>>>>>> as a logical system.


    It corrects the divergence of classical and symbolic logic from
    correct reasoning.

    This makes you system not much more than a toy for most people.

    Note, that at least by some meanings of your words, it could be >>>>>>>>> construed that you only accept as a correct deductive argument, >>>>>>>>> and arguement whose premises can at least some times be true, >>>>>>>>> but there are some statements we don't know if they CAN be
    sometimes true, so your logic system would seem to not allow >>>>>>>>> doing logic with that sort of statement.


    An analytic statement is only known to be true when it is
    derived by applying only truth preserving operations to all of >>>>>>>> its premises and all of its premises are known to be true,
    otherwise its truth value is unknown.


    KNOWN to be True, not IS TRUE.

    It remains unknown until it is known to be true or false.
    My system only eliminates impossibly true or false.


    So, you don't know what is still valid to use?



    Your statement even admits that truth value might be unknow,
    which might allow it to even be UNKNOWABLE (maybe just in that
    system) if it can't be proven or refuted.


    unprovable in the system means untrue in the system.

    And what does 'untrue' mean?


    Untrue means the same thing as Prolog's negation as failure.

    Which means... ?

    Prolog, as I remember, ASSUMES that anything not provable is FALSE
    (not 'untrue').


    Unprovable means untrue and does not mean false in Prolog.


    We know that there is a number that solves an equation, but we
    don't know that number, or how to compute that number.

    Can we say that it is true that such a number exists?


    If you defined your terms correctly, then yes because this has been
    stipulated in your deinitions.

    This means that we can define the floor of that number, which will
    be an integer (call it N), is it true that this number exists?

    That interger, MUST be either even or odd, so we know that either
    iseven(N) is true or isodd(N) is true.

    By your logic, the 'truth value' of both of those must be 'untrue'
    since we can not prove which one it is.

    This is the sort of problem you run into with your system.


    There is NOTHING about an analytic statement that says it can
    only be true if it is provable. Note, "its truth value is
    unknown" doesn't mean it doesn't have a truth value, just that we >>>>>>> don't know what that value is.


    Within any formal system unprovable in the system means untrue in
    the system.

    The entire body of analytic truth is constructed only on the basis >>>>>> of semantic connections between expressions of language, or
    expressions that are stipulated to have the semantic property of
    Boolean true. Lacking both of these and the expression is untrue.

    Since axioms are provable on the basis that they are axioms then
    both of these factors that make an expression true also make it
    provable.


    You clearly are just stating words by rote and not actually
    understanding them.


    There are only two possible ways that any analytical expression of
    language can possibly be true:
    (1) It is stipulated to be true.
    (2) It is derived by applying only truth preserving operations to
    (1) or the consequences of (2).

    So there exists an integer number N is neither Even or Odd? (it is
    untrue for both tests)

    I don't think you actually understand what that means.


    Analytic Truth is truth that is provable, that is correct, but it
    accepts that there is OTHER things that happen to be true but are
    not provable.


    Analytic truth includes every expression of language that can be
    completely verified as totally true entirely on the basis of its
    meaning without requiring any sense data from the sense organs.

    Empirical expressions of language also require sense data from the
    sense organs to verify their truth.

    You still don't understand, do you.

    You still confuse Truth with Knowledge.
    There are only two possible ways that any analytical expression of
    language can possibly be true:
    (1) It is stipulated to be true.
    (2) It is derived by applying only truth preserving operations to (1)
    or the consequences of (2).

    Try and provide an example of a possible truth that does not require
    one of those two.


    The result of applying the operation of replacing N by N/2 if  N is even
    or by 3N+1 if N is odd will eventually get you to the number 1 for all Natural numbers N > 0.

    This statement MUST be either True or False, by its nature, there is no
    other possible state.

    This statement seems to be true, but it has unable to be proven to be true.

    Yes, we can not validly USE the idea that this statement is true to
    prove something else, because we know that it is still possible that it
    won't be true. But we CAN use that it will either be true or false to
    show something.

    That is an analytical expression that isn't proven to be an analytical
    truth, but it may still be true,

    Probably an unconscious strawman error, that does not contradict my
    original claim because it is a strawman error.

    True(x) iff Stipulated_True(x) or Proven_True(x)
    I am referring to <is> true and you are referring to <might be> true,
    they are not the same.



    --
    Copyright 2022 Pete Olcott

    "Talent hits a target no one else can hit;
    Genius hits a target no one else can see."
    Arthur Schopenhauer

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Richard Damon@21:1/5 to olcott on Fri May 13 19:14:10 2022
    XPost: comp.theory, sci.logic, sci.lang.semantics

    On 5/13/22 6:23 PM, olcott wrote:
    On 5/13/2022 5:14 PM, Richard Damon wrote:
    On 5/13/22 5:53 PM, olcott wrote:
    On 5/13/2022 4:30 PM, Richard Damon wrote:
    On 5/13/22 4:56 PM, olcott wrote:
    On 5/13/2022 3:43 PM, Richard Damon wrote:
    On 5/13/22 3:43 PM, olcott wrote:
    On 5/13/2022 2:13 PM, Richard Damon wrote:
    On 5/13/22 2:10 PM, olcott wrote:
    On 5/13/2022 12:47 PM, Richard Damon wrote:
    On 5/13/22 1:20 PM, olcott wrote:
    *Validity and Soundness*
    A deductive argument is said to be valid if and only if it >>>>>>>>>>> takes a form that makes it impossible for the premises to be >>>>>>>>>>> true and the conclusion nevertheless to be false. Otherwise, >>>>>>>>>>> a deductive argument is said to be invalid.
    https://iep.utm.edu/val-snd/

    If the Moon is made of green cheese then all dogs are cats is >>>>>>>>>>> valid and even though premises and conclusion are
    semantically unrelated.

    *Here is my correction to that issue*
    A deductive argument is said to be valid if and only if it >>>>>>>>>>> takes a form such that its conclusion is a necessary
    consequence of all of its premises.


    And, have you done the basic investigation to find out how >>>>>>>>>> much of conventional logic you invalidate with that change? >>>>>>>>>>

    It categorically changes everything that is broken.

    So, you are saying we need to throw out EVERYTHING we know and >>>>>>>> start over?


    Change everything that diverges from my spec:
    A deductive argument is said to be valid if and only if it takes >>>>>>> a form such that its conclusion is a necessary consequence of all >>>>>>> of its premises.

    I think, especially with the comment below, people will decide >>>>>>>> that your "new" logic systm isn't worth the cost to switch to. >>>>>>>>

    Note, that it may be hard to define "necessary consequence" in >>>>>>>>>> a formal matter.


    {A,B} ⊢ C only when truth preserving operations are applied to >>>>>>>>> {A,B} to derive C.

    And what do you define truth perserving as?


    Semantic relevance is maintained.

    Normally the phrase means that True Premises always generate
    True Results (which means the statement "If the moon is made of >>>>>>>> green cheese then ll dogs are cats" IS Truth Preserving, since >>>>>>>> any time the premise is true (never) the conclusion is true.


    It should be noted that your example, while considered an
    vaild inference by normal logic, can never be used to actually >>>>>>>>>> prove its conclusion, so doesn't actually cause problems in >>>>>>>>>> normal logic (can you show a case where it does?)


    With my correction true and unprovable is impossible,
    unprovable simply means untrue.


    Ok, then you have just stated that your new logic system can't >>>>>>>> handle mathematics, and thus "Computer SCience" no longer exists >>>>>>>> as a logical system.


    It corrects the divergence of classical and symbolic logic from
    correct reasoning.

    This makes you system not much more than a toy for most people. >>>>>>>>
    Note, that at least by some meanings of your words, it could >>>>>>>>>> be construed that you only accept as a correct deductive
    argument, and arguement whose premises can at least some times >>>>>>>>>> be true, but there are some statements we don't know if they >>>>>>>>>> CAN be sometimes true, so your logic system would seem to not >>>>>>>>>> allow doing logic with that sort of statement.


    An analytic statement is only known to be true when it is
    derived by applying only truth preserving operations to all of >>>>>>>>> its premises and all of its premises are known to be true,
    otherwise its truth value is unknown.


    KNOWN to be True, not IS TRUE.

    It remains unknown until it is known to be true or false.
    My system only eliminates impossibly true or false.


    So, you don't know what is still valid to use?



    Your statement even admits that truth value might be unknow,
    which might allow it to even be UNKNOWABLE (maybe just in that >>>>>>>> system) if it can't be proven or refuted.


    unprovable in the system means untrue in the system.

    And what does 'untrue' mean?


    Untrue means the same thing as Prolog's negation as failure.

    Which means... ?

    Prolog, as I remember, ASSUMES that anything not provable is FALSE
    (not 'untrue').


    Unprovable means untrue and does not mean false in Prolog.


    We know that there is a number that solves an equation, but we
    don't know that number, or how to compute that number.

    Can we say that it is true that such a number exists?


    If you defined your terms correctly, then yes because this has been
    stipulated in your deinitions.

    This means that we can define the floor of that number, which will >>>>>> be an integer (call it N), is it true that this number exists?

    That interger, MUST be either even or odd, so we know that either
    iseven(N) is true or isodd(N) is true.

    By your logic, the 'truth value' of both of those must be 'untrue' >>>>>> since we can not prove which one it is.

    This is the sort of problem you run into with your system.


    There is NOTHING about an analytic statement that says it can
    only be true if it is provable. Note, "its truth value is
    unknown" doesn't mean it doesn't have a truth value, just that >>>>>>>> we don't know what that value is.


    Within any formal system unprovable in the system means untrue in >>>>>>> the system.

    The entire body of analytic truth is constructed only on the
    basis of semantic connections between expressions of language, or >>>>>>> expressions that are stipulated to have the semantic property of >>>>>>> Boolean true. Lacking both of these and the expression is untrue. >>>>>>>
    Since axioms are provable on the basis that they are axioms then >>>>>>> both of these factors that make an expression true also make it
    provable.


    You clearly are just stating words by rote and not actually
    understanding them.


    There are only two possible ways that any analytical expression of
    language can possibly be true:
    (1) It is stipulated to be true.
    (2) It is derived by applying only truth preserving operations to
    (1) or the consequences of (2).

    So there exists an integer number N is neither Even or Odd? (it is
    untrue for both tests)

    I don't think you actually understand what that means.


    Analytic Truth is truth that is provable, that is correct, but it
    accepts that there is OTHER things that happen to be true but are
    not provable.


    Analytic truth includes every expression of language that can be
    completely verified as totally true entirely on the basis of its
    meaning without requiring any sense data from the sense organs.

    Empirical expressions of language also require sense data from the
    sense organs to verify their truth.

    You still don't understand, do you.

    You still confuse Truth with Knowledge.
    There are only two possible ways that any analytical expression of
    language can possibly be true:
    (1) It is stipulated to be true.
    (2) It is derived by applying only truth preserving operations to (1)
    or the consequences of (2).

    Try and provide an example of a possible truth that does not require
    one of those two.


    The result of applying the operation of replacing N by N/2 if  N is
    even or by 3N+1 if N is odd will eventually get you to the number 1
    for all Natural numbers N > 0.

    This statement MUST be either True or False, by its nature, there is
    no other possible state.

    This statement seems to be true, but it has unable to be proven to be
    true.

    Yes, we can not validly USE the idea that this statement is true to
    prove something else, because we know that it is still possible that
    it won't be true. But we CAN use that it will either be true or false
    to show something.

    That is an analytical expression that isn't proven to be an analytical
    truth, but it may still be true,

    Probably an unconscious strawman error, that does not contradict my
    original claim because it is a strawman error.

    True(x) iff Stipulated_True(x) or Proven_True(x)
    I am referring to <is> true and you are referring to <might be> true,
    they are not the same.


    Then why dod you say "Possible truth", if you meant an ACTUAL truth.

    How about;

    x: there exist a number N that the 3N+1 / N/2 pattern never gets to 1

    True(x | ~x) is KNOWN to be true, but isn't a Stipulated Truth or a
    Proven Truth by your rules.

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From olcott@21:1/5 to Richard Damon on Fri May 13 18:20:06 2022
    XPost: comp.theory, sci.logic, sci.lang.semantics

    On 5/13/2022 6:14 PM, Richard Damon wrote:
    On 5/13/22 6:23 PM, olcott wrote:
    On 5/13/2022 5:14 PM, Richard Damon wrote:
    On 5/13/22 5:53 PM, olcott wrote:
    On 5/13/2022 4:30 PM, Richard Damon wrote:
    On 5/13/22 4:56 PM, olcott wrote:
    On 5/13/2022 3:43 PM, Richard Damon wrote:
    On 5/13/22 3:43 PM, olcott wrote:
    On 5/13/2022 2:13 PM, Richard Damon wrote:
    On 5/13/22 2:10 PM, olcott wrote:
    On 5/13/2022 12:47 PM, Richard Damon wrote:
    On 5/13/22 1:20 PM, olcott wrote:
    *Validity and Soundness*
    A deductive argument is said to be valid if and only if it >>>>>>>>>>>> takes a form that makes it impossible for the premises to be >>>>>>>>>>>> true and the conclusion nevertheless to be false. Otherwise, >>>>>>>>>>>> a deductive argument is said to be invalid.
    https://iep.utm.edu/val-snd/

    If the Moon is made of green cheese then all dogs are cats >>>>>>>>>>>> is valid and even though premises and conclusion are
    semantically unrelated.

    *Here is my correction to that issue*
    A deductive argument is said to be valid if and only if it >>>>>>>>>>>> takes a form such that its conclusion is a necessary
    consequence of all of its premises.


    And, have you done the basic investigation to find out how >>>>>>>>>>> much of conventional logic you invalidate with that change? >>>>>>>>>>>

    It categorically changes everything that is broken.

    So, you are saying we need to throw out EVERYTHING we know and >>>>>>>>> start over?


    Change everything that diverges from my spec:
    A deductive argument is said to be valid if and only if it takes >>>>>>>> a form such that its conclusion is a necessary consequence of
    all of its premises.

    I think, especially with the comment below, people will decide >>>>>>>>> that your "new" logic systm isn't worth the cost to switch to. >>>>>>>>>

    Note, that it may be hard to define "necessary consequence" >>>>>>>>>>> in a formal matter.


    {A,B} ⊢ C only when truth preserving operations are applied to >>>>>>>>>> {A,B} to derive C.

    And what do you define truth perserving as?


    Semantic relevance is maintained.

    Normally the phrase means that True Premises always generate >>>>>>>>> True Results (which means the statement "If the moon is made of >>>>>>>>> green cheese then ll dogs are cats" IS Truth Preserving, since >>>>>>>>> any time the premise is true (never) the conclusion is true. >>>>>>>>>

    It should be noted that your example, while considered an >>>>>>>>>>> vaild inference by normal logic, can never be used to
    actually prove its conclusion, so doesn't actually cause >>>>>>>>>>> problems in normal logic (can you show a case where it does?) >>>>>>>>>>>

    With my correction true and unprovable is impossible,
    unprovable simply means untrue.


    Ok, then you have just stated that your new logic system can't >>>>>>>>> handle mathematics, and thus "Computer SCience" no longer
    exists as a logical system.


    It corrects the divergence of classical and symbolic logic from >>>>>>>> correct reasoning.

    This makes you system not much more than a toy for most people. >>>>>>>>>
    Note, that at least by some meanings of your words, it could >>>>>>>>>>> be construed that you only accept as a correct deductive >>>>>>>>>>> argument, and arguement whose premises can at least some >>>>>>>>>>> times be true, but there are some statements we don't know if >>>>>>>>>>> they CAN be sometimes true, so your logic system would seem >>>>>>>>>>> to not allow doing logic with that sort of statement.


    An analytic statement is only known to be true when it is
    derived by applying only truth preserving operations to all of >>>>>>>>>> its premises and all of its premises are known to be true, >>>>>>>>>> otherwise its truth value is unknown.


    KNOWN to be True, not IS TRUE.

    It remains unknown until it is known to be true or false.
    My system only eliminates impossibly true or false.


    So, you don't know what is still valid to use?



    Your statement even admits that truth value might be unknow, >>>>>>>>> which might allow it to even be UNKNOWABLE (maybe just in that >>>>>>>>> system) if it can't be proven or refuted.


    unprovable in the system means untrue in the system.

    And what does 'untrue' mean?


    Untrue means the same thing as Prolog's negation as failure.

    Which means... ?

    Prolog, as I remember, ASSUMES that anything not provable is FALSE
    (not 'untrue').


    Unprovable means untrue and does not mean false in Prolog.


    We know that there is a number that solves an equation, but we
    don't know that number, or how to compute that number.

    Can we say that it is true that such a number exists?


    If you defined your terms correctly, then yes because this has
    been stipulated in your deinitions.

    This means that we can define the floor of that number, which
    will be an integer (call it N), is it true that this number exists? >>>>>>>
    That interger, MUST be either even or odd, so we know that either >>>>>>> iseven(N) is true or isodd(N) is true.

    By your logic, the 'truth value' of both of those must be
    'untrue' since we can not prove which one it is.

    This is the sort of problem you run into with your system.


    There is NOTHING about an analytic statement that says it can >>>>>>>>> only be true if it is provable. Note, "its truth value is
    unknown" doesn't mean it doesn't have a truth value, just that >>>>>>>>> we don't know what that value is.


    Within any formal system unprovable in the system means untrue >>>>>>>> in the system.

    The entire body of analytic truth is constructed only on the
    basis of semantic connections between expressions of language, >>>>>>>> or expressions that are stipulated to have the semantic property >>>>>>>> of Boolean true. Lacking both of these and the expression is
    untrue.

    Since axioms are provable on the basis that they are axioms then >>>>>>>> both of these factors that make an expression true also make it >>>>>>>> provable.


    You clearly are just stating words by rote and not actually
    understanding them.


    There are only two possible ways that any analytical expression of >>>>>> language can possibly be true:
    (1) It is stipulated to be true.
    (2) It is derived by applying only truth preserving operations to
    (1) or the consequences of (2).

    So there exists an integer number N is neither Even or Odd? (it is
    untrue for both tests)

    I don't think you actually understand what that means.


    Analytic Truth is truth that is provable, that is correct, but it >>>>>>> accepts that there is OTHER things that happen to be true but are >>>>>>> not provable.


    Analytic truth includes every expression of language that can be
    completely verified as totally true entirely on the basis of its
    meaning without requiring any sense data from the sense organs.

    Empirical expressions of language also require sense data from the >>>>>> sense organs to verify their truth.

    You still don't understand, do you.

    You still confuse Truth with Knowledge.
    There are only two possible ways that any analytical expression of
    language can possibly be true:
    (1) It is stipulated to be true.
    (2) It is derived by applying only truth preserving operations to (1)
    or the consequences of (2).

    Try and provide an example of a possible truth that does not require
    one of those two.


    The result of applying the operation of replacing N by N/2 if  N is
    even or by 3N+1 if N is odd will eventually get you to the number 1
    for all Natural numbers N > 0.

    This statement MUST be either True or False, by its nature, there is
    no other possible state.

    This statement seems to be true, but it has unable to be proven to be
    true.

    Yes, we can not validly USE the idea that this statement is true to
    prove something else, because we know that it is still possible that
    it won't be true. But we CAN use that it will either be true or false
    to show something.

    That is an analytical expression that isn't proven to be an
    analytical truth, but it may still be true,

    Probably an unconscious strawman error, that does not contradict my
    original claim because it is a strawman error.

    True(x) iff Stipulated_True(x) or Proven_True(x)
    I am referring to <is> true and you are referring to <might be> true,
    they are not the same.


    Then why dod you say "Possible truth", if you meant an ACTUAL truth.


    My system rejects expressions of language that are impossibly true such
    as expressions that are true and unprovable.

    How about;

    x: there exist a number N that the 3N+1 / N/2 pattern never gets to 1

    True(x | ~x) is KNOWN to be true, but isn't a Stipulated Truth or a
    Proven Truth by your rules.



    --
    Copyright 2022 Pete Olcott

    "Talent hits a target no one else can hit;
    Genius hits a target no one else can see."
    Arthur Schopenhauer

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  • From Richard Damon@21:1/5 to olcott on Fri May 13 20:15:24 2022
    XPost: comp.theory, sci.logic, sci.lang.semantics

    On 5/13/22 7:20 PM, olcott wrote:
    On 5/13/2022 6:14 PM, Richard Damon wrote:
    On 5/13/22 6:23 PM, olcott wrote:
    On 5/13/2022 5:14 PM, Richard Damon wrote:
    On 5/13/22 5:53 PM, olcott wrote:
    On 5/13/2022 4:30 PM, Richard Damon wrote:
    On 5/13/22 4:56 PM, olcott wrote:
    On 5/13/2022 3:43 PM, Richard Damon wrote:
    On 5/13/22 3:43 PM, olcott wrote:
    On 5/13/2022 2:13 PM, Richard Damon wrote:
    On 5/13/22 2:10 PM, olcott wrote:
    On 5/13/2022 12:47 PM, Richard Damon wrote:
    On 5/13/22 1:20 PM, olcott wrote:
    *Validity and Soundness*
    A deductive argument is said to be valid if and only if it >>>>>>>>>>>>> takes a form that makes it impossible for the premises to >>>>>>>>>>>>> be true and the conclusion nevertheless to be false. >>>>>>>>>>>>> Otherwise, a deductive argument is said to be invalid. >>>>>>>>>>>>> https://iep.utm.edu/val-snd/

    If the Moon is made of green cheese then all dogs are cats >>>>>>>>>>>>> is valid and even though premises and conclusion are >>>>>>>>>>>>> semantically unrelated.

    *Here is my correction to that issue*
    A deductive argument is said to be valid if and only if it >>>>>>>>>>>>> takes a form such that its conclusion is a necessary >>>>>>>>>>>>> consequence of all of its premises.


    And, have you done the basic investigation to find out how >>>>>>>>>>>> much of conventional logic you invalidate with that change? >>>>>>>>>>>>

    It categorically changes everything that is broken.

    So, you are saying we need to throw out EVERYTHING we know and >>>>>>>>>> start over?


    Change everything that diverges from my spec:
    A deductive argument is said to be valid if and only if it
    takes a form such that its conclusion is a necessary
    consequence of all of its premises.

    I think, especially with the comment below, people will decide >>>>>>>>>> that your "new" logic systm isn't worth the cost to switch to. >>>>>>>>>>

    Note, that it may be hard to define "necessary consequence" >>>>>>>>>>>> in a formal matter.


    {A,B} ⊢ C only when truth preserving operations are applied >>>>>>>>>>> to {A,B} to derive C.

    And what do you define truth perserving as?


    Semantic relevance is maintained.

    Normally the phrase means that True Premises always generate >>>>>>>>>> True Results (which means the statement "If the moon is made >>>>>>>>>> of green cheese then ll dogs are cats" IS Truth Preserving, >>>>>>>>>> since any time the premise is true (never) the conclusion is >>>>>>>>>> true.


    It should be noted that your example, while considered an >>>>>>>>>>>> vaild inference by normal logic, can never be used to
    actually prove its conclusion, so doesn't actually cause >>>>>>>>>>>> problems in normal logic (can you show a case where it does?) >>>>>>>>>>>>

    With my correction true and unprovable is impossible,
    unprovable simply means untrue.


    Ok, then you have just stated that your new logic system can't >>>>>>>>>> handle mathematics, and thus "Computer SCience" no longer
    exists as a logical system.


    It corrects the divergence of classical and symbolic logic from >>>>>>>>> correct reasoning.

    This makes you system not much more than a toy for most people. >>>>>>>>>>
    Note, that at least by some meanings of your words, it could >>>>>>>>>>>> be construed that you only accept as a correct deductive >>>>>>>>>>>> argument, and arguement whose premises can at least some >>>>>>>>>>>> times be true, but there are some statements we don't know >>>>>>>>>>>> if they CAN be sometimes true, so your logic system would >>>>>>>>>>>> seem to not allow doing logic with that sort of statement. >>>>>>>>>>>>

    An analytic statement is only known to be true when it is >>>>>>>>>>> derived by applying only truth preserving operations to all >>>>>>>>>>> of its premises and all of its premises are known to be true, >>>>>>>>>>> otherwise its truth value is unknown.


    KNOWN to be True, not IS TRUE.

    It remains unknown until it is known to be true or false.
    My system only eliminates impossibly true or false.


    So, you don't know what is still valid to use?



    Your statement even admits that truth value might be unknow, >>>>>>>>>> which might allow it to even be UNKNOWABLE (maybe just in that >>>>>>>>>> system) if it can't be proven or refuted.


    unprovable in the system means untrue in the system.

    And what does 'untrue' mean?


    Untrue means the same thing as Prolog's negation as failure.

    Which means... ?

    Prolog, as I remember, ASSUMES that anything not provable is FALSE >>>>>> (not 'untrue').


    Unprovable means untrue and does not mean false in Prolog.


    We know that there is a number that solves an equation, but we >>>>>>>> don't know that number, or how to compute that number.

    Can we say that it is true that such a number exists?


    If you defined your terms correctly, then yes because this has
    been stipulated in your deinitions.

    This means that we can define the floor of that number, which
    will be an integer (call it N), is it true that this number exists? >>>>>>>>
    That interger, MUST be either even or odd, so we know that
    either iseven(N) is true or isodd(N) is true.

    By your logic, the 'truth value' of both of those must be
    'untrue' since we can not prove which one it is.

    This is the sort of problem you run into with your system.


    There is NOTHING about an analytic statement that says it can >>>>>>>>>> only be true if it is provable. Note, "its truth value is
    unknown" doesn't mean it doesn't have a truth value, just that >>>>>>>>>> we don't know what that value is.


    Within any formal system unprovable in the system means untrue >>>>>>>>> in the system.

    The entire body of analytic truth is constructed only on the >>>>>>>>> basis of semantic connections between expressions of language, >>>>>>>>> or expressions that are stipulated to have the semantic
    property of Boolean true. Lacking both of these and the
    expression is untrue.

    Since axioms are provable on the basis that they are axioms
    then both of these factors that make an expression true also >>>>>>>>> make it provable.


    You clearly are just stating words by rote and not actually
    understanding them.


    There are only two possible ways that any analytical expression
    of language can possibly be true:
    (1) It is stipulated to be true.
    (2) It is derived by applying only truth preserving operations to >>>>>>> (1) or the consequences of (2).

    So there exists an integer number N is neither Even or Odd? (it is >>>>>> untrue for both tests)

    I don't think you actually understand what that means.


    Analytic Truth is truth that is provable, that is correct, but >>>>>>>> it accepts that there is OTHER things that happen to be true but >>>>>>>> are not provable.


    Analytic truth includes every expression of language that can be >>>>>>> completely verified as totally true entirely on the basis of its >>>>>>> meaning without requiring any sense data from the sense organs.

    Empirical expressions of language also require sense data from
    the sense organs to verify their truth.

    You still don't understand, do you.

    You still confuse Truth with Knowledge.
    There are only two possible ways that any analytical expression of
    language can possibly be true:
    (1) It is stipulated to be true.
    (2) It is derived by applying only truth preserving operations to (1) >>>>> or the consequences of (2).

    Try and provide an example of a possible truth that does not
    require one of those two.


    The result of applying the operation of replacing N by N/2 if  N is
    even or by 3N+1 if N is odd will eventually get you to the number 1
    for all Natural numbers N > 0.

    This statement MUST be either True or False, by its nature, there is
    no other possible state.

    This statement seems to be true, but it has unable to be proven to
    be true.

    Yes, we can not validly USE the idea that this statement is true to
    prove something else, because we know that it is still possible that
    it won't be true. But we CAN use that it will either be true or
    false to show something.

    That is an analytical expression that isn't proven to be an
    analytical truth, but it may still be true,

    Probably an unconscious strawman error, that does not contradict my
    original claim because it is a strawman error.

    True(x) iff Stipulated_True(x) or Proven_True(x)
    I am referring to <is> true and you are referring to <might be> true,
    they are not the same.


    Then why dod you say "Possible truth", if you meant an ACTUAL truth.


    My system rejects expressions of language that are impossibly true such
    as expressions that are true and unprovable.


    So, you are playing Humpty Dumpty?

    It sounds like you are just insisting on the axiom that True is
    Provable, which is NOT an axiom that is part of Computation Theory, and
    in fact has been proven that if added to this sort of field of logic
    makes the system inconssistent, and by your definition that makes it
    inccorect.

    That means you axiom is incorrect and thus WRONG.

    You are proving that you are ignorant of how logic works because your
    mind is just too smal to understand.

    "Your System" is not the system in use in Formal Logic, especially not Computation Theory as a branch of Mathematics. Until you understand
    that, you are just going to continue making a FOOL of yourself as you
    make claims that are just not true in the system that you claim to be
    working (Remember, in an existing logic system, you don't get to change
    the rules).

    How about;

    x: there exist a number N that the 3N+1 / N/2 pattern never gets to 1

    True(x | ~x) is KNOWN to be true, but isn't a Stipulated Truth or a
    Proven Truth by your rules.




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